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Superman (1978 film)

Superman (also marketed as Superman: The Movie) is a 1978 superhero film based on the DC Comics superhero Superman, played by Christopher Reeve. It is the first of four installments in the Superman film series starring Reeve as Superman. The film was directed by Richard Donner based on a screenplay by Mario Puzo, David Newman, Leslie Newman, and Robert Benton. In addition to Reeve, the film features an ensemble cast including Marlon Brando, Gene Hackman, Jeff East, Margot Kidder, Glenn Ford, Phyllis Thaxter, Jackie Cooper, Trevor Howard, Marc McClure, Terence Stamp, Valerie Perrine, Ned Beatty, Jack O'Halloran, Maria Schell, and Sarah Douglas. It depicts the origin of Superman, including his infancy as Kal-El of Krypton, son of Jor-El (Brando), and his youthful years in the rural town of Smallville. Disguised as reporter Clark Kent, he adopts a mild-mannered disposition in Metropolis and develops a romance with Lois Lane (Kidder) while battling the villainous Lex Luthor (Hackman).

Ilya Salkind had the idea of a Superman film in 1973 and, after a difficult process with DC Comics, the Salkinds bought the rights to the character the following year. Several directors, most notably Guy Hamilton, and screenwriters were associated with the project before Donner was hired to direct. Tom Mankiewicz was drafted in to rewrite the script and was given a creative consultant credit. It was decided to film both Superman and its sequel Superman II (1980) simultaneously, with principal photography beginning in March 1977 and ending in October 1978. Tensions arose between Donner and the producers, and a decision was made to stop filming the sequel, of which 75 percent had already been completed, and finish the first film.

The most expensive film made up to that point, with a budget of $55 million, Superman premiered at The Kennedy Center in Washington, DC, on December 10, 1978, and was released in the United Kingdom on December 14, and in the United States on December 15. The film was a critical and financial success; its worldwide box office earnings of $300 million made it the second-highest-grossing release of the year. It received praise for Reeve's performance and John Williams's musical score, and was nominated for Best Film Editing, Best Music (Original Score), and Best Sound at the 51st Academy Awards, and received a Special Achievement Academy Award for Visual Effects. Groundbreaking in its use of special effects and science fiction/fantasy storytelling, the film's legacy presaged the mainstream popularity of Hollywood's superhero film franchises. In 2017, Superman was selected for preservation by the Library of Congress's National Film Registry.

Plot
On the planet Krypton, Jor-El, a member of the Kryptonian high council, sentences criminals General Zod, Non, and Ursa to the Phantom Zone. He warns the council that Krypton will be destroyed by its exploding red supergiant sun, but they dismiss his concerns. Before the planet's destruction, Jor-El and his wife Lara send their baby son Kal-El to Earth, where his unique physiology grants him evolving superhuman abilities. Kal-El's spaceship touches down near Smallville, Kansas. Found by Jonathan and Martha Kent, who are astonished when the infant lifts their truck, they adopt him, naming him Clark. As he grows, hiding his powers, Jonathan believes Clark was sent to Earth for a special purpose.

Soon after Jonathan's fatal heart attack, a glowing green crystal from his spaceship that is hidden in the barn calls to him. This leads him to the Arctic, where a Fortress of Solitude, echoing Krypton's architecture, ascends from the ice. Inside, Jor-El's hologram reveals Clark's heritage and trains him for twelve years. Emerging in a blue-and-red suit bearing the House of El crest, he is cautioned against changing human history.

Clark is hired as a reporter for the Daily Planet in Metropolis. He is drawn to Lois Lane. After saving her from a helicopter accident, Clark secretly uses his powers in public acts of heroism, gaining immediate fame as the "caped wonder". Perry White, the Daily Planet's chief, seeks more information on this new hero. Clark later visits Lois, taking her on a flight, leading her to coin his name, "Superman".

Criminal mastermind Lex Luthor discovers a joint U.S. Army/U.S. Navy missile test and plots to target the San Andreas Fault with reprogrammed missiles, though one is misdirected by his bumbling assistant, Otis. Suspecting Superman's interference, Lex identifies a Kryptonian meteorite, lethal to Superman. With Otis and his girlfriend Eve Teschmacher, Lex retrieves it and traps Superman in his lair, revealing his plan to sink the western U.S., making his desert land prime coastline. He weakens Superman using the meteor, now known as Kryptonite, and informs him of the misdirected missile set for Hackensack, New Jersey.

Concerned for her mother in Hackensack, Teschmacher frees Superman, urging him to first stop the eastbound missile. He sends it to space but misses the westbound missile, which triggers severe earthquakes in California, endangering landmarks like the Golden Gate Bridge and Hoover Dam. Superman counteracts the devastation by mending the fault line. As Superman rescues others, Lois is trapped in her car by an aftershock, suffocating before he can save her. Distraught and enraged over his failure to save Lois, Superman disregards Jor-El's warning against altering history. Heeding Jonathan's belief in his purpose, he flies around Earth, reversing time to prevent Lois's death and the missile's destruction. After saving the West Coast, he imprisons Luthor and Otis, then soars into the sunrise.

Cast

 * Marlon Brando as Jor-El: Superman's biological father on Krypton. He has a theory about the planet exploding, yet the Council refuses to listen. He dies as the planet explodes but successfully sends his infant son to Earth as a means to help the child. Brando sued the Salkinds and Warner Bros. for $50 million because he felt cheated out of his share of the box office profits. This stopped Brando's footage from being used in Richard Lester's version of Superman II.
 * Gene Hackman as Lex Luthor: A scientific genius and businessman who is Superman's nemesis. It is he who discovers Superman's weakness and hatches a plan that puts millions of people in danger.
 * Christopher Reeve as Clark Kent / Superman: Born on Krypton as Kal-El and raised on Earth, he is a being of immense power, strength, flight and invulnerability who, after realizing his destiny to serve mankind, uses his powers to protect and save others. As a means to protect his identity, he works in Metropolis at the Daily Planet as mild-mannered newspaper reporter Clark Kent and changes his clothes into a red-blue red caped suit with an S shield on its chest and is dubbed "Superman" by Lois. Reeve was picked from over 200 actors who auditioned for the role.
 * Jeff East as the teenage Clark Kent: As a teenager, he is forced to hide his superhuman abilities, making him unpopular among his classmates and frustrating his efforts to gain the attention of classmate Lana Lang (Diane Sherry). Following the death of his adoptive father, he travels to the Arctic to discover his Kryptonian heritage. East's dialogue in the film is redubbed by Christopher Reeve for the final cut.
 * Ned Beatty as Otis: Lex Luthor's bumbling henchman.
 * Jackie Cooper as Perry White: Clark Kent's hot-tempered boss at the Daily Planet. He assigns Lois to uncover the news of an unknown businessman purchasing a large amount of property in California. Keenan Wynn was originally cast, but dropped out shortly before filming because of heart disease. Cooper, who originally auditioned for Otis, was subsequently cast.
 * Glenn Ford as Jonathan Kent: Clark Kent's adoptive father in Smallville during his youth. He is a farmer who teaches Clark skills that will help him in the future. He later has a fatal heart attack that changes Clark's outlook on his duty to others.
 * Trevor Howard as the First Elder: Head of the Kryptonian Council, who does not believe Jor-El's claim that Krypton is doomed. He warns Jor-El: "Any attempt by you to create a climate of fear and panic amongst the populace must be deemed by us an act of insurrection."
 * Margot Kidder as Lois Lane: A reporter at the Daily Planet, who becomes a romantic interest to Clark Kent. The producers and director had a very specific concept for Lois: liberated, hard-nosed, witty and attractive. Kidder was cast because her performance had a certain spark and vitality, and because of her strong interaction with Christopher Reeve. Over 100 actresses were considered for the role. Margot Kidder (suggested by Stalmaster), Anne Archer, Susan Blakely, Lesley Ann Warren, Deborah Raffin and Stockard Channing screen tested from March through May 1977. The final decision was between Channing and Kidder, with the latter winning the role.
 * Jack O'Halloran as Non: Large and mute, the third of the Kryptonian villains who are sentenced to be isolated in the Phantom Zone.
 * Valerie Perrine as Eve Teschmacher: Lex Luthor's girlfriend and accomplice. Already cynical of his increasing grandiosity and disturbed by his cruelty, she saves Superman's life after learning that Luthor has launched a nuclear missile toward her mother's hometown of Hackensack, New Jersey. She shows a romantic interest in Superman, implied by her fixing her hair before she makes her presence known to him, and then by kissing him before she saves his life.
 * Maria Schell as Vond-Ah: Like Jor-El, a top Kryptonian scientist; but she too is not swayed by Jor-El's theories.
 * Terence Stamp as General Zod: Evil leader of the three Kryptonian criminals who swears vengeance against Jor-El when he is sentenced to the Phantom Zone. His appearance was to set him and his accomplices as the main antagonists of Superman II.
 * Phyllis Thaxter as Martha Kent (née Clark): Clark Kent's faithful adoptive mother. A kindly woman who dotes on her adoptive son and is fiercely devoted to her husband, Jonathan. She is her son's emotional support after Clark is devastated by Jonathan's death. Thaxter was producer Ilya Salkind's mother-in-law.
 * Susannah York as Lara: Superman's biological mother on Krypton. She, after learning of Krypton's fate, has apprehensions about sending her infant son to a strange planet alone.
 * Marc McClure as Jimmy Olsen: A teenage photographer at the Daily Planet. Jeff East, who portrayed the teenage Clark Kent, originally auditioned for this role but outranked following his portrayal of the teen Clark.
 * Sarah Douglas as Ursa: General Zod's second in command and consort, sentenced to the Phantom Zone for her unethical scientific experiments. Caroline Munro turned down the opportunity to play Ursa, in favour of Naomi in The Spy Who Loved Me.
 * Harry Andrews as the Second Elder: Council member, who urges Jor-El to be reasonable about plans to save Krypton.

Kirk Alyn and Noel Neill have cameo appearances (they played the parents of young Lois Lane in a deleted scene that was restored in later home media releases). Alyn and Neill portrayed Superman and Lois Lane in the film serials Superman (1948) and Atom Man vs. Superman (1950), and were the first actors to portray the characters onscreen in a live-action format. Neill reprised her role in the 1950s Adventures of Superman TV series.

Larry Hagman and Rex Reed also make cameos; Hagman plays an army major in charge of a convoy that is transporting one of the missiles, and Reed plays himself as he meets Lois and Clark outside the Daily Planet headquarters.

Development
Ilya Salkind had first conceived the idea for a Superman film in late 1973. In November 1974, after a long, difficult process with DC Comics, the Superman film rights were purchased by Ilya, his father Alexander Salkind, and their partner Pierre Spengler. DC wanted a list of actors that were to be considered for Superman, and approved the producer's choices of Muhammad Ali, Al Pacino, James Caan, Steve McQueen, Clint Eastwood and Dustin Hoffman. The filmmakers felt it was best to film Superman and Superman II back-to-back, and to make a negative pickup deal with Warner Bros. William Goldman was approached to write the screenplay, while Leigh Brackett was considered. Ilya hired Alfred Bester, who began writing a film treatment. Alexander felt, however, that Bester was not famous enough, so he hired Mario Puzo to write the screenplay at a $600,000 salary. Francis Ford Coppola, William Friedkin, Richard Lester (who later directed Superman II and III), Peter Yates, John Guillermin, Ronald Neame and Sam Peckinpah were in negotiations to direct. Peckinpah dropped out when he produced a gun during a meeting with Ilya. George Lucas turned down the offer because of his commitment to Star Wars.

Ilya wanted to hire Steven Spielberg to direct, but Alexander was skeptical, feeling it was best to "wait until [Spielberg's] big fish opens." Jaws was very successful, prompting the producers to offer Spielberg the position, but by then Spielberg had already committed to Close Encounters of the Third Kind. Guy Hamilton was hired as director, while Puzo delivered his script for Superman and Superman II in July 1975. Jax-Ur appeared as one of General Zod's henchmen, with Clark Kent written as a television reporter. Dustin Hoffman, who was previously considered for Superman, turned down Lex Luthor.

In early 1975, Brando signed on as Jor-El with a salary of $3.7 million and 11.75% of the box office gross profits, totaling $19 million. He horrified Salkind by proposing in their first meeting that Jor-El appear as a green suitcase or a bagel with Brando's voice, but Donner used flattery to persuade the actor to portray Jor-El himself. Brando hoped to use some of his salary for a proposed 13-part Roots-style miniseries on Native Americans in the United States. Brando had it in his contract to complete all of his scenes in twelve days. He also refused to memorize his dialogue, so cue cards were compiled across the set. Fellow Oscar winner Hackman was cast as Lex Luthor days later. The filmmakers made it a priority to shoot all of Brando's and Hackman's footage "because they would be committed to other films immediately." Though the Salkinds felt that Puzo had written a solid story for the two-part film, they deemed his scripts as "very heavy", and so hired Robert Benton and David Newman for rewrite work. Benton became too busy directing The Late Show, so David's wife Leslie was brought in to help her husband finish writing duties. George MacDonald Fraser was later hired to do some work on the script, but he says he did little.

Their script was submitted in July 1976, and had a camp tone, including a cameo appearance by Telly Savalas as his Kojak character. The scripts for Superman and Superman II were now at over 400 pages combined. Pre-production started at Cinecittà Studios in Rome, with sets starting construction and flying tests being unsuccessfully experimented. "In Italy", producer Ilya Salkind remembered, "we lost about $2 million [on flying tests]." Marlon Brando found out he could not film in Italy because of a warrant out for his arrest: a sexual-obscenity charge from Last Tango in Paris. Production moved to England in late 1976, but Hamilton could not join because he was a tax exile. Hamilton left the project as he was also ill.

Mark Robson was strongly considered and was in talks to direct, but after seeing The Omen, the producers hired Richard Donner. Donner had previously been planning Damien: Omen II when he was hired in January 1977 for $1 million to direct Superman and Superman II. Donner felt it was best to start from scratch. "They had prepared the picture for a year and not one bit was useful to me." Donner was dissatisfied with the campy script and brought in Tom Mankiewicz to perform a rewrite. According to Mankiewicz, "not a word from the Puzo script was used." "It was a well-written, but still a ridiculous script. It was 550 pages. I said, 'You can't shoot this screenplay because you'll be shooting for five years'", Donner continued. "That was literally a shooting script and they planned to shoot all 550 pages. You know, 110 pages is plenty for a script, so even for two features, that was way too much." Mankiewicz conceived having each Kryptonian family wear a crest resembling a different letter, justifying the 'S' on Superman's costume. The Writers Guild of America refused to credit Mankiewicz for his rewrites, so Donner gave him a creative consultant credit, much to the annoyance of the Guild.

Casting of Superman
It was initially decided to first sign an A-list actor for Superman before Richard Donner was hired as director. Robert Redford was offered a large sum, but felt he was too famous. Burt Reynolds also turned down the role, while Sylvester Stallone was interested and met with Donner, but he was more interested casting an "unknown" actor. Paul Newman was offered his choice of roles as Superman, Lex Luthor or Jor-El for $4 million, turning down all three roles.

When it was next decided to cast an unknown actor, casting director Lynn Stalmaster first suggested Christopher Reeve, but Donner and the producers felt he was too young and skinny. Over 200 unknown actors auditioned for Superman.

Olympic champion Bruce Jenner auditioned for the title role. Patrick Wayne was cast, but dropped out when his father John Wayne was diagnosed with stomach cancer.

Both Neil Diamond and Arnold Schwarzenegger lobbied hard for the role, but were ignored. James Caan, James Brolin, Lyle Waggoner, Christopher Walken, Nick Nolte, Jon Voight, and Perry King were approached. Nolte wanted to play Superman as a schizophrenic. Kris Kristofferson and Charles Bronson were also considered for the title role. Warren Beatty was offered the role but turned it down.

James Caan said he was offered the part but turned it down. "I just couldn't wear that suit."

"We found guys with fabulous physique who couldn't act or wonderful actors who did not look remotely like Superman", creative consultant Tom Mankiewicz remembered. The search became so desperate that producer Ilya Salkind's wife's dentist was screen tested.

Stalmaster convinced Donner and Ilya to have Reeve screen test in February 1977. Reeve stunned the director and producers, but he was told to wear a "muscle suit" to produce the desired muscular physique. Reeve refused, undertaking a strict physical exercise regime headed by David Prowse. Prowse had wanted to portray Superman, but was denied an audition by the filmmakers because he was not American. Prowse also auditioned for Non. Reeve went from 188 lb to 212 lb during pre-production and filming. Reeve earned only $250,000 for both Superman and Superman II, while his veteran co-stars received huge sums of money: $3.7 million for Brando and $2 million for Hackman for Superman. However, Reeve felt, "Superman brought me many opportunities, rather than closing a door in my face." Jeff East portrays teenage Clark Kent. East's lines were overdubbed by Reeve during post-production. "I was not happy about it because the producers never told me what they had in mind", East commented. "It was done without my permission but it turned out to be okay. Chris did a good job but it caused tension between us. We resolved our issues with each other years later." East also tore several thigh muscles when performing the stunt of racing alongside the train. Technicians applied 3 to 4 hours of prosthetic makeup daily to increase his resemblance to Reeve.

Filming
Principal photography began on March 28, 1977, at Pinewood Studios for the Krypton scenes, budgeted as the most expensive film ever made at that point, which was $55 million. Because Superman was being shot simultaneously with Superman II, filming lasted nineteen months, until October 1978. Filming was originally scheduled to last between seven and eight months, but problems arose during production. John Barry served as production designer, while Stuart Craig and Norman Reynolds worked as art directors. Derek Meddings and Les Bowie were credited as visual effects supervisors. Stuart Freeborn was the make-up artist, while Barry, David Tomblin, John Glen, David Lane, Robert Lynn and an uncredited Peter Duffell and André de Toth directed second unit scenes. Vic Armstrong was hired as the stunt coordinator and Reeve's stunt double; his wife Wendy Leech was Kidder's double. Superman was also the final complete film by cinematographer Geoffrey Unsworth, who died during post-production while working on Tess for director Roman Polanski. The Fortress of Solitude was constructed at Shepperton Studios and at Pinewood's 007 Stage. Upon viewing the footage of Krypton, Warner Bros. decided to distribute in not only North America, but also in foreign countries. Due to complications and problems during filming, Warner Bros. also supplied $20 million and acquired television rights.

New York City doubled for Metropolis, while the New York Daily News Building served as the location for the offices of the Daily Planet. Brooklyn Heights was also used. Filming in New York lasted five weeks, during the time of the New York City blackout of 1977. Production moved to Alberta for scenes set in Smallville, with the cemetery scene filmed in the canyon of Beynon, Alberta, the high school football scenes at Barons, Alberta, and the Kent farm constructed at Blackie, Alberta. Brief filming also took place in Gallup, New Mexico; Lake Mead; and Grand Central Terminal. Director Donner had tensions with the Salkinds and Spengler concerning the escalating production budget and the shooting schedule. Creative consultant Tom Mankiewicz reflected, "Donner never got a budget or a schedule. He was constantly told he was way over schedule and budget. At one point he said, 'Why don't you just schedule the film for the next two days, and then I'll be nine months over?'" Richard Lester, who worked with the Salkinds on The Three Musketeers and The Four Musketeers, was then brought in as a temporary co-producer to mediate the relationship between Donner and the Salkinds, who by now were refusing to talk to each other. On his relationship with Spengler, Donner remarked, "At one time if I'd seen him, I would have killed him."

Lester was offered producing credit but refused, going uncredited for his work. Salkind felt that bringing a second director onto the set meant there would be someone ready in the event that Donner could not fulfill his directing duties. "Being there all the time meant he [Lester] could take over", Salkind admitted. "[Donner] couldn't make up his mind on stuff." On Lester, Donner reflected, "He'd been suing the Salkinds for his money on Three and Four Musketeers, which he'd never gotten. He won a lot of his lawsuits, but each time he sued the Salkinds in one country, they'd move to another, from Costa Rica to Panama to Switzerland. When I was hired, Lester told me, 'Don't do it. Don't work for them. I was told not to, but I did it. Now I'm telling you not to, but you'll probably do it and end up telling the next guy.' Lester came in as a 'go-between'. I didn't trust Lester, and I told him. He said, 'Believe me, I'm only doing it because they're paying me the money that they owe me from the lawsuit. I'll never come onto your set unless you ask me; I'll never go to your dailies. If I can help you in any way, call me."

It was decided to stop shooting Superman II and focus on finishing Superman. Donner had already completed 75% of the sequel. The filmmakers took a risk: if Superman was a box office bomb, they would not finish Superman II. The original climax for Superman II had General Zod, Ursa, and Non destroying the planet, with Superman time traveling to fix the damage.

Donner commented, "I decided if Superman is a success, they're going to do a sequel. If it ain't a success, a cliffhanger ain't gonna bring them to see Superman II."

Effects
Superman contains large-scale visual effects sequences. The Golden Gate Bridge scale model stood 70 ft long and 20 ft high. Other miniatures included the Krypton Council Dome and the Hoover Dam. Slow motion was used to simulate the vast amount of water for the Hoover Dam destruction. The Fortress of Solitude was a combination of a full-scale set and matte paintings. The car crashes on the Golden Gate Bridge were a mixture of models and stunt drivers on a disused runway. Young Clark Kent's long-distance football punt was executed with a wooden football loaded into an air blaster placed in the ground. The Superman costume was to be a much darker blue, but the use of blue screen made it transparent.

As detailed in the Superman: The Movie DVD special effects documentary "The Magic Behind The Cape", presented by optical effects supervisor Roy Field, in the end, three techniques were used to achieve the flying effects.

For landings and take-offs, wire flying-riggings were devised and used. On location, these were suspended from tower cranes, whereas in the studio elaborate rigs were suspended from the studio ceilings. Some of the wire-flying work was quite audacious—the penultimate shot where Superman flies out of the prison yard, for example. Although stuntmen were used, Reeve did much of the work himself, and was suspended as high as 50 ft in the air. Counterweights and pulleys were typically used to achieve flying movement, rather than electronic or motorized devices. The thin wires used to suspend Reeve were typically removed from the film in post-production using rotoscope techniques, although this wasn't necessary in all shots (in certain lighting conditions or when Superman is very distant in the frame, the wires were more or less imperceptible).

For stationary shots where Superman is seen flying toward or away from the camera, blue screen matte techniques were used. Reeve would be photographed suspended against a blue screen. While a special device made his cape flap to give the illusion of movement, the actor himself would remain stationary (save for banking his body). Instead, the camera would use a mixture of long zoom-ins and zoom-outs and dolly in/dolly outs to cause him to become larger or smaller in the frame. The blue background would then be photochemically removed and Reeve's isolated image would be inserted into a matted area of a background plate shot. The zoom-ins or zoom-outs would give the appearance of flying away or toward the contents of the background plate. The disparity in lighting and color between the matted image and the background plate, the occasional presence of black matte lines (where the matte area and the matted image—in this case, Superman—do not exactly match up), and the slightly unconvincing impression of movement achieved through the use of zoom lenses is characteristic of these shots.

Where the shot is tracking with Superman as he flies (such as in the Superman and Lois Metropolis flying sequence), front projection was used. This involved photographing the actors suspended in front of a background image dimly projected from the front onto a special screen made by 3M that would reflect light back directly into a combined camera/projector. The result was a very clear and intense photographic reproduction of both the actors and the background plate, with far less image deterioration or lighting problems than occur with rear projection.

A technique was developed that combined the front projection effect with specially designed zoom lenses. The illusion of movement was created by zooming in on Reeve while making the front projected image appear to recede. For scenes where Superman interacts with other people or objects while in flight, Reeve and actors were put in a variety of rigging equipment with careful lighting and photography. This also led to the creation of the Zoptic system.

The highly reflective costumes worn by the Kryptonians are made of the same 3M material used for the front projection screens and were the result of an accident during Superman flying tests. "We noticed the material lit up on its own", Donner explained. "We tore the material into tiny pieces and glued it on the costumes, designing a front projection effect for each camera. There was a little light on each camera, and it would project into a mirror, bounce out in front of the lens, hit the costume, [and] millions of little glass beads would light up and bring the image back into the camera."

The Clio Award-winning opening titles were made with traditional optical animation using an innovative technique that combined a motion control camera with slit-scan photography. The titles were designed by Richard Greenberg of R/Greenberg Associates (R/GA)

Music
Jerry Goldsmith, who scored Donner's The Omen, was originally set to compose Superman. Portions of Jerry Goldsmith's work from Planet of the Apes were used in Superman 's teaser trailer. He dropped out over scheduling conflicts, and John Williams was hired. Williams conducted the London Symphony Orchestra to record the soundtrack. The music was one of the last pieces to come into place. Williams' "Theme from Superman (Main Title)" was released as a single, reaching #81 on the U.S. Billboard Hot 100 and #69 Cash Box. Williams liked that the film did not take itself too seriously and that it had a theatrical camp feel to it.

Kidder was supposed to sing "Can You Read My Mind?", the lyrics to which were written by Leslie Bricusse, but Donner disliked it and changed it to a composition accompanied by a voiceover. Maureen McGovern eventually recorded the single, "Can You Read My Mind?" in 1979, although the song did not appear on the film soundtrack. It became a mid-chart hit on the Billboard Hot 100 that year (#52), spending three weeks at number five on the U.S. Adult Contemporary chart, as well as making lesser appearances on the corresponding Canadian charts. It was also a very minor hit on the U.S. Country chart, reaching #93. Both Williams' and McGovern's singles contained theme music from the score. The score earned John Williams an Academy Award nomination, but he lost to Giorgio Moroder's score for Midnight Express.

The soundtrack was originally released as a 2-LP set in December 1978, and the same recording was issued on CD for the first time in 1987 (with the tracks "Growing Up" and "Lex Luthor's Lair" omitted to fit the recording onto one disc).

A re-recording of the score, conducted by John Debney and performed by the Royal Scottish National Orchestra, was released by Varese Sarabande records in 1998. In 2000, an expanded edition of the original score was released on a 2-CD set by Rhino Records.

In February 2008, Film Score Monthly released an 8-CD boxed set titled Superman: The Music, including a newly restored complete score on the first two discs, as well as alternates and source cues on disc 8. As part of the film's 40th anniversary in February 2019, La-La Land Records released the fully expanded restoration of Williams' score on a 3-disc set, including the previously issued alternates and source music.

Themes
Superman is divided into three basic sections, each having a distinct theme and visual style. The first segment, set on Krypton, is meant to be typical of science fiction films, but also lays the groundwork for an analogy that emerges in the relationship between Jor-El and Kal-El. The second segment, set in Smallville, is reminiscent of 1950s films, and its small-town atmosphere is meant to evoke a Norman Rockwell painting. The third (and largest) segment, set mostly in Metropolis, was an attempt to present the superhero story with as much realism as possible (what Donner called "verisimilitude"), relying on traditional cinematic drama and using only subtle humor instead of a campy approach.

In each of the three acts, the mythic status of Superman is enhanced by events that recall the hero's journey (or monomyth) as described by Joseph Campbell. Each act has a discernible cycle of "call" and journey. The journey is from Krypton to Earth in the first act, from Smallville to the Fortress of Solitude in the second act, and then from Metropolis to the whole world in the third act.

Many have noted the examples of apparent Christian symbolism. Donner, Tom Mankiewicz and Ilya Salkind have commented on the use of Christian references to discuss the themes of Superman. Mankiewicz deliberately fostered analogies with Jor-El (God) and Kal-El (Jesus). Donner is somewhat skeptical of Mankiewicz's actions, joking "I got enough death threats because of that."

Several concepts and items of imagery have been used in Biblical comparisons. Jor-El casts out General Zod from Krypton, a parallel to the casting out of Satan from Heaven. The spacecraft that brings Kal-El to Earth is in the form of a star (Star of Bethlehem). Kal-El comes to Jonathan and Martha Kent, who are unable to have children. Martha Kent states, "All these years how we've prayed and prayed that the good Lord would see fit to give us a child", which was compared to the Virgin Mary.

Mirroring Biblical accounts of Jesus, Clark travels into the wilderness to find out who he is and what he has to do. Jor-El says, "Live as one of them, Kal-El, to discover where your strength and power are needed. But always hold in your heart the pride of your special heritage. They can be a great people, Kal-El, and they wish to be. They only lack the light to show the way. For this reason above all, their capacity for good, I have sent them you, my only son." The theme resembles the Biblical account of God sending his only son Jesus to Earth in hope for the good of mankind. More were seen when Donner was able to complete Superman II: The Richard Donner Cut, featuring the fall, resurrection and his battle with evil. Another vision was that of The Creation of Adam.

The Christian imagery in the Reeve films has provoked comment on the Jewish origins of Superman. Rabbi Simcha Weinstein's book Up, Up and Oy Vey: How Jewish History, Culture and Values Shaped the Comic Book Superhero, says that Superman is both a pillar of society and one whose cape conceals a "nebbish", saying "He's a bumbling, nebbish Jewish stereotype. He's Woody Allen." Ironically, it is also in the Reeve films that Clark Kent's persona has the greatest resemblance to Woody Allen, though his conscious model was Cary Grant's character in Bringing Up Baby. This same theme is pursued about 1940s superheroes generally in Disguised as Clark Kent: Jews, Comics, and the Creation of the Superhero by Danny Fingeroth.

In the scene where Lois Lane interviews Superman on the balcony, Superman replies, "I never lie." Salkind felt this was an important point in the film, since Superman, living under his secret identity as Clark Kent, is "telling the biggest lie of all time." His romance with Lois also leads him to contradict Jor-El's orders to avoid altering human history, time traveling to save her from dying. Superman instead takes the advice of Jonathan Kent, his father on Earth.

Release
Superman was originally scheduled to be released in June 1978, the 40th anniversary of Action Comics 1, which first introduced Superman, but the problems during filming pushed the film back by six months. Editor Stuart Baird reflected, "Filming was finished in October 1978 and it is a miracle we had the film released two months later. Big-budgeted films today tend to take six to eight months." Donner, for his part, wished that he had "had another six months; I would have perfected a lot of things. But at some point, you've gotta turn the picture over."

Warner Bros. Pictures spent $6–7 million on marketing the film. Superman premiered at the Uptown Theater in Washington, D.C., on December 10, 1978, with director Richard Donner and several cast members in attendance. Three days later, on December 13, it had a European Royal Charity Premiere at the Empire, Leicester Square in London, with Queen Elizabeth II and Prince Andrew in attendance.

Box office
It set a new all-time U.S. industry record for business during a pre-Christmas week with $12 million, and set new records for Warner Bros. for their best opening day ($2.8 million) and three-day weekend ($7.5 million). For the week of December 22–28, it set an all-time U.S. weekly record of $18.5 million. It also set a record single day gross for Warner Bros. with a gross of $3.8 million. In its third weekend it grossed $13.1 million for the four-day holiday weekend setting a record 18-day gross of $43.7 million.

Approximately 120 million people saw Superman in the opening theatrical run in 1978. Including re-releases, it went on to gross $134.5 million in the United States and Canada, and $166 million internationally, totaling $300.5 million worldwide. Superman was the highest-grossing film of 1978 in North America. It was also Warner Bros.'s most successful film at the time.

Critical response
Superman received mostly positive reviews from critics. According to Rotten Tomatoes, of  critics gave Superman a positive review, with an average rating of. The website's critical consensus reads, "Superman deftly blends humor and gravitas, taking advantage of the perfectly cast Reeve to craft a loving, nostalgic tribute to an American pop culture icon." Metacritic assigned the film a weighted average score of 81 out of 100, based on 19 critics, indicating "universal acclaim". The film was widely regarded as one of the top ten films of 1978. Superman creators Jerry Siegel and Joe Shuster, in tears, thanked Donner and gave a positive reaction. Shuster was "delighted to see Superman on the screen. I got chills. Chris Reeve has just the right touch of humor. He really is Superman." Siegel beamed, "It's exactly as I imagined it."

Roger Ebert gave the film four out of four stars. Although describing the Krypton scenes as "ponderous" ("Brando was allegedly paid $3 million for his role, or, judging by his dialogue, $500,000 a cliché"), Ebert wrote that "Superman is a pure delight, a wondrous combination of all the old-fashioned things we never really get tired of: adventure and romance, heroes and villains, earthshaking special effects, and – you know what else? Wit". He praised Reeve, stating that he "sells the role; wrong casting here would have sunk everything", and concluded that the film "works so well because of its wit and its special effects". Ebert placed the film on his ten best list of 1978. He would later go on to place it on his "Great Movies" list. Gene Siskel of the Chicago Tribune gave the film three stars out of four, calling it "a delightful mess. Good performances. Sloppy editing. Cheap nonflying special effects. Funny dialog. In sum, Superman is the kind of picture critics tear apart, but still say, 'You ought to see it.

James Harwood of Variety called the film "a wonderful, chuckling, preposterously exciting fantasy", and further added: "As both the wholesome man of steel and his bumbling secret identity Clark Kent, Reeve is excellent." Vincent Canby of The New York Times wrote in a mixed review, "The Superman comic strip has been carefully, elaborately, sometimes wittily blown up for the big-theater screen, which, though busy, often seems sort of empty." Charles Champlin of the Los Angeles Times called the film "a big letdown", praising Reeve as "the salvaging strength of the film" but referring to the matter of the villain as "an essential problem", finding that "even in a succession of wigs, Gene Hackman is not preposterous, funny or dementedly menacing, and what he's doing here is not evident." Gary Arnold of The Washington Post wrote in a positive review, "Despite a lull here and a lapse there, this superproduction turns out to be prodigiously inventive and enjoyable, doubly blessed by sophisticated illusionists behind the cameras and a brilliant new stellar personality in front of the cameras—Christopher Reeve, a young actor at once handsome and astute enough to rationalize the preposterous fancy of a comic-book superhero in the flesh."

Writing in a retrospective review, James Berardinelli believed "there's no doubt that it's a flawed movie, but it's one of the most wonderfully entertaining flawed movies made during the 1970s. It's exactly what comic book fans hoped it would be. Perhaps most heartening of all, however, is the message at the end of the credits announcing the impending arrival of Superman II." Harry Knowles is a longtime fan of the film, but was critical of elements that did not represent the Superman stories as seen in the comics. Neal Gabler similarly felt that the film focused too much on shallow comedy. He also argued that the film should have adhered more to the spirit of Mario Puzo's original script, and referred to the first three Superman films collectively as "simply puffed-up TV episodes."

Accolades
Superman was nominated for three Academy Awards: Best Film Editing (Stuart Baird), Best Original Score (John Williams) and Best Sound (Gordon K. McCallum, Graham V. Hartstone, Nicolas Le Messurier and Roy Charman) and received a Special Achievement Academy Award for its visual effects. Donner publicly expressed disgust that production designer John Barry and cinematographer Geoffrey Unsworth had not been recognized by the Academy.

Superman was also successful at the 32nd British Academy Film Awards. Reeve won Best Newcomer, while Hackman, Unsworth, Barry, and the sound designers earned nominations. The film won the Hugo Award for Best Dramatic Presentation. At the Saturn Awards, Kidder, Barry, John Williams, and the visual effects department received awards, and the film won Best Science Fiction Film. Reeve, Hackman, Donner, Valerie Perrine, and costume designer Yvonne Blake were nominated for their work as well. In addition, Williams was nominated at the 36th Golden Globe Awards and won the Grammy Award for Best Score Soundtrack for Visual Media.

The extended TV version
While, by contract, Richard Donner had major editorial control over what was theatrically released, the Salkinds had editorial control on what was shown outside of theaters. This was the result of deals that had been made between the producers and the ABC television network prior to the film's release. Financially, the more footage that was restored for television, the more revenue that could be made for the broadcast (the producers charged by the minute for every bit of footage added back in). During production of the film, Alexander and Ilya Salkind found themselves in the position of having to sell more and more of their rights back to Warner Bros. in exchange for financial help, which is why Warner Bros. had theatrical and home video distribution rights. By 1981, when the television rights reverted to the Salkinds, the producers had already prepared a 3-hour-and-8-minute version that actually had been the first version of the film visually locked down prior to being re-edited for theatrical release. This extended cut, which would be used for worldwide television distribution, reincorporated some 45 minutes of footage and music deleted from the theatrical cut. Networks and stations could then re-edit their own version at their discretion. This edit is commonly known as the "Salkind International Television Cut".

ABC aired the broadcast television debut of Superman over two nights in February 1982, with a majority of the unused footage. The 182-minute network cut (which was slightly cut down for content) was repeated in November of that same year, this time in its entirety in one evening. ABC presented the original theatrical version of the film for the two remaining broadcasts.

When the TV rights reverted to Warner Bros. in 1985, CBS aired the film one last time on network television in its theatrical version. When the movie entered the syndication market in 1988 (following a play-out run on pay cable ) TV stations were offered the extended cut or the theatrical cut. The stations that showed the extended cut edited the second half to add more advertising time and "previously on..." cutback scenes just as ABC had done in 1982.

In 1994 (following a pay-cable reissue and its obligatory run on USA Network), Warner Bros. Television syndicated the full 188-minute international television version, most famously on Los Angeles station KCOP. The most notable additions unseen on U.S. television were two additional scenes never seen before, in addition to what had been previously reinstated. This version also surfaced outside of Los Angeles. For example, WJLA Channel 7, an ABC affiliate in Washington, D.C., aired the extended cut in July 1994. Because its first known airing was on the aforementioned KCOP, it is also known in fan circles as the "KCOP Version".

There were various extended TV versions each broadcast in various countries. Most of these are in pan and scan, as they were made in the 1980s, when films were not letterboxed to preserve the theatrical aspect ratio on old TVs.

Until 2017, it was thought the quality of the extended network TV version was inferior to any theatrical or previous home video release because it was mastered in 16mm (using the "film chain system") and a mono sound mix done, as by the time the extended cut was prepared in 1981, stereo was not available in television broadcasts (16 mm television prints were, in fact, made and mastered on NTSC Standard Definition video for the initial ABC network broadcasts). However, during an inventory of the Warner Bros. library, an IP master of the full 188-minute television version was discovered. This eighteen-reel master was not marked with an aspect ratio, but the print was inspected and, as it turned out, was in the proper 2.35:1 Panavision ratio. This was the source of the Warner Archive Collection Blu-Ray release of what would officially be called the "Superman: The Movie Extended Cut", issued on October 3, 2017. The video release was visually restored by WB's imaging department, and, other than the opening and end credits (which are in true stereo), the film is presented in an enhanced version of the mono TV sound mix. This particular release also includes another version discussed below.

Richard Donner was critical of this extended cut of the film. He called this version of the film "terrible," saying it "was nothing more than an assembly." He said he cut the bad material out of the movie and that the producers and Warner Bros. added it back in just "to make a buck."

Other editions
When Michael Thau and Warner Home Video started working on a film restoration in 2000, only eight minutes of the added footage that had been used in the TV cut could be considered restored into a version that director Richard Donner called his preferred version of the film. Thau determined that some of the extra footage could not be added because of poor visual effects. Thau felt "the pace of the film's storyline would be adversely affected [and there were] timing problems matching [footage] with John Williams' musical score, etc… The cut of the movie shown on KCOP was put together to make the movie longer when shown on TV as the Television Station paid per minute to air the movie. The "Special Edition" cut is designed for the best viewing experience in the true spirit of movie making." There was a special test screening of the Special Edition in 2001 in San Antonio, Texas, on March 23 with plans for a possible wider theatrical release later that year, which did not occur. In May 2001, Warner Home Video released the special edition on DVD. Director Donner also assisted, working slightly over a year on the project. The release included making-of documentaries directed by Thau and eight minutes of restored footage.

Thau explained, "I worked on Ladyhawke and that's how I really met Dick [Donner] and Tom Mankiewicz. I used to hear those wonderful stories in the cutting room that Tom and Dick and Stuart would tell about Superman and that's how I kind of got the ideas for the plots of 'Taking Flight' and 'Making Superman'". Donner commented, "There are a few shots where Chris [Reeve]'s costume looked green. We went in and cleaned that up, bringing the color back to where it should be." Thau wanted to make the film shorter: "I wanted to take out the damn poem where Lois is reciting a poem ("Can You Read My Mind") when they're flying around. I also wanted to take out a lot of that car chase where it was just generic action... It was like a two-minute car chase. But Dick didn't want to take [that] out [or] the poem." It was followed by a box set release in the same month, containing "bare bones" editions of Superman II, Superman III, and Superman IV: The Quest for Peace. In November 2006, a four-disc special edition was released, followed by an HD DVD release and Blu-ray. Also available (with other films) is the nine-disc "Christopher Reeve Superman Collection" and the 14-disc "Superman Ultimate Collector's Edition".

On November 6, 2018 (following year-long worldwide revival theatrical screenings to commemorate the 40th anniversary of the film's original release), Warner Bros. Home Entertainment released an Ultra HD Blu-ray of Superman presented in a new Dolby Vision transfer of the original theatrical version straight from the original camera negative, with its original 70mm/six-track stereo mix rendered in 5.1 surround, in addition to the 2000 remix in Dolby Atmos. This new release also includes a standard Blu-ray Disc of the theatrical cut, plus select bonus features carried over from previous video releases.

Legacy
In 2007, the Visual Effects Society listed Superman as the 44th-most influential use of visual effects of all time. In 2008, Empire magazine named it the 174th-greatest film of all time on its list of 500. In 2009, Entertainment Weekly ranked Superman 3rd on their list of The All-Time Coolest Heroes in Pop Culture.

With the film's success, it was immediately decided to finish Superman II. Ilya and Alexander Salkind and Pierre Spengler did not ask Donner to return because Donner had criticized them during the film's publicity phase. Donner commented in January 1979, "I'd work with Spengler again, but only on my terms. As long as he has nothing to say as the producer, and is just liaison between Alexander Salkind and his money, that's fine. If they don't want it on those terms, then they need to go out and find another director, it sure as shit ain't gonna be me." Kidder, who portrayed Lois Lane, was dissatisfied by the producers' decision, and also criticized the Salkinds during publicity. Kidder said that as a result, she was only given a cameo appearance for Superman III, and not a main supporting role. Jack O'Halloran, who portrayed Non, stated, "It was great to work with Donner. Richard Lester was as big an asshole as the Salkinds." Two more films, Superman III (1983) and Superman IV: The Quest for Peace (1987), were produced. Donner's vision for Superman II was eventually realized nearly three decades later, when he supervised the editing of Superman II: The Richard Donner Cut, which was released in 2006. In the same year, Donner and writer Geoff Johns wrote "Last Son", a comic book story arc in Action Comics featuring Superman. Unused footage of Marlon Brando as Jor-El, discovered during the restoration of Superman II: The Richard Donner Cut, was used in Superman Returns (2006).

Because Superman went into production prior to the releases of Star Wars (May 1977) and Close Encounters of the Third Kind (November 1977), some observers credit the three films collectively for launching the reemergence of a large market for science fiction films in the 1980s. This is certainly the view of Superman producer Ilya Salkind and some who have interviewed him, as well as of film production assistant Brad Lohan. Other observers of film history tend to credit the resurgence of science fiction films simply to the Lucas and Spielberg productions, and see Superman as the first of the new cycle of films launched by the first two. Ilya Salkind denies any connection between Superman—which began filming in March 1977—and the other films, stating that "I did not know about ' Star Wars '; ' Star Wars ' did not know about ' Superman '; ' Close Encounters ' did not know about 'Superman.' It really was completely independent—nobody knew anything about anybody." Superman also established the superhero film genre as viable outside the production of low-budget Saturday matinee serials. Director Christopher Nolan cited Richard Donner's vision and scope of Superman when pitching the concept for Batman Begins to Warner Bros. in 2002. The film's influence can also be seen in films of the genre including the X-Men films, Sam Raimi's Spider-Man (2002), and Patty Jenkins' Wonder Woman (2017).

In 2021, DC Comics revived the continuity of the 1978 film with their Superman '78 comic book series, emulating the look of the Christopher Reeve films. The series picks up where the first two films left off, thereby acting as a direct sequel.

After the first screening of the DC Extended Universe (DCEU) film The Flash (2023) to the attendees of the Cinemacon 2023, director Andy Muschietti and producer Barbara Muschietti revealed that a cameo appearance of Brando's Jor-El from Superman was considered for the film, but was left in the "cutting floor room" due to not fitting in the story.

The film inspired The Kinks' 1979 song "(Wish I Could Fly Like) Superman", when the band's main songwriter, Ray Davies, watched the film in late 1978.

The film is recognized by American Film Institute in these lists:
 * 2003: AFI's 100 Years...100 Heroes & Villains:
 * Superman (Clark Kent) – #26 Hero

In December 2017, the film was selected for preservation by the United States Library of Congress National Film Registry, for being "culturally, historically or aesthetically significant".

title: Superman (1978 film)


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Heat death of the universe

The heat death of the universe (also known as the Big Chill or Big Freeze) is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy, and will therefore be unable to sustain processes that increase entropy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium.

If the curvature of the universe is hyperbolic or flat, or if dark energy is a positive cosmological constant, the universe will continue expanding forever, and a heat death is expected to occur, with the universe cooling to approach equilibrium at a very low temperature after a long time period.

The hypothesis of heat death stems from the ideas of Lord Kelvin who, in the 1850s, took the theory of heat as mechanical energy loss in nature (as embodied in the first two laws of thermodynamics) and extrapolated it to larger processes on a universal scale. This also allowed Kelvin to formulate the heat death paradox, which disproves an infinitely old universe.

Origins of the idea
The idea of heat death stems from the second law of thermodynamics, of which one version states that entropy tends to increase in an isolated system. From this, the hypothesis implies that if the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, according to this hypothesis, there is a tendency in nature towards the dissipation (energy transformation) of mechanical energy (motion) into thermal energy; hence, by extrapolation, there exists the view that, in time, the mechanical movement of the universe will run down as work is converted to heat because of the second law.

The conjecture that all bodies in the universe cool off, eventually becoming too cold to support life, seems to have been first put forward by the French astronomer Jean Sylvain Bailly in 1777 in his writings on the history of astronomy and in the ensuing correspondence with Voltaire. In Bailly's view, all planets have an internal heat and are now at some particular stage of cooling. Jupiter, for instance, is still too hot for life to arise there for thousands of years, while the Moon is already too cold. The final state, in this view, is described as one of "equilibrium" in which all motion ceases.

The idea of heat death as a consequence of the laws of thermodynamics, however, was first proposed in loose terms beginning in 1851 by Lord Kelvin (William Thomson), who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843) and Rudolf Clausius (1850). Thomson's views were then elaborated over the next decade by Hermann von Helmholtz and William Rankine.

History
The idea of the heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851, Lord Kelvin outlined the view, as based on recent experiments on the dynamical theory of heat: "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."

In 1852, Thomson published On a Universal Tendency in Nature to the Dissipation of Mechanical Energy, in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will naturally tend to dissipate or run down. The ideas in this paper, in relation to their application to the age of the Sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject. In 1862, Thomson published "On the age of the Sun's heat", an article in which he reiterated his fundamental beliefs in the indestructibility of energy (the first law) and the universal dissipation of energy (the second law), leading to diffusion of heat, cessation of useful motion (work), and exhaustion of potential energy, "lost irrecoverably" through the material universe, while clarifying his view of the consequences for the universe as a whole. Thomson wrote:

"The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever." The clock's example shows how Kelvin was unsure whether the universe would eventually achieve thermodynamic equilibrium. Thompson later speculated that restoring the dissipated energy in "vis viva" and then usable work – and therefore revert the clock's direction, resulting in a "rejuvenating universe" – would require "a creative act or an act possessing similar power". Starting from this publication, Kelvin also introduced the heat death paradox (Kelvin's paradox), which challenged the classical concept of an infinitely old universe, since the universe has not achieved its thermodynamic equilibrium, thus further work and entropy production are still possible. The existence of stars and temperature differences can be considered an empirical proof that the universe is not infinitely old.

In the years to follow both Thomson's 1852 and the 1862 papers, Helmholtz and Rankine both credited Thomson with the idea, along with his paradox, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a "heat death" (Helmholtz), which will be the "end of all physical phenomena" (Rankine).

Current status
Proposals about the final state of the universe depend on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a hypothesized "open" or "flat" universe that continues expanding indefinitely, either a heat death or a Big Rip is expected to eventually occur. If the cosmological constant is zero, the universe will approach absolute zero temperature over a very long timescale. However, if the cosmological constant is positive, the temperature will asymptote to a non-zero positive value, and the universe will approach a state of maximum entropy in which no further work is possible.

Time frame for heat death
The theory suggests that from the "Big Bang" through the present day, matter and dark matter in the universe are thought to have been concentrated in stars, galaxies, and galaxy clusters, and are presumed to continue to do so well into the future. Therefore, the universe is not in thermodynamic equilibrium, and objects can do physical work. :§VID The decay time for a supermassive black hole of roughly 1 galaxy mass (1011 solar masses) because of Hawking radiation is in the order of 10100 years, so entropy can be produced until at least that time. Some large black holes in the universe are predicted to continue to grow up to perhaps 1014 during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10106 years. After that time, the universe enters the so-called Dark Era and is expected to consist chiefly of a dilute gas of photons and leptons. :§VIA With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long timescales. Speculatively, it is possible that the universe may enter a second inflationary epoch, or assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state. :§VE It is also possible that entropy production will cease and the universe will reach heat death. :§VID

It is suggested that, over vast periods of time, a spontaneous entropy decrease would eventually occur via the Poincaré recurrence theorem, thermal fluctuations,  and fluctuation theorem. Through this, another universe could possibly be created by random quantum fluctuations or quantum tunnelling in roughly $$10^{10^{10^{56}}}$$ years.

Opposing views
Max Planck wrote that the phrase "entropy of the universe" has no meaning because it admits of no accurate definition. In 2008, Walter Grandy wrote: "It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence." According to László Tisza, "If an isolated system is not in equilibrium, we cannot associate an entropy with it." Hans Adolf Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system". According to Giovanni Gallavotti, "there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state". Discussing the question of entropy for non-equilibrium states in general, Elliott H. Lieb and Jakob Yngvason express their opinion as follows: "Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way." In Peter Landsberg's opinion: "The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. ... These questions have a certain fascination, but the answers are speculations."

A 2010 analysis of entropy states, "The entropy of a general gravitational field is still not known", and "gravitational entropy is difficult to quantify". The analysis considers several possible assumptions that would be needed for estimates and suggests that the observable universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. Lee Smolin goes further: "It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems." This point of view is also supported by the fact of a recent experimental discovery of a stable non-equilibrium steady state in a relatively simple closed system. It should be expected that an isolated system fragmented into subsystems does not necessarily come to thermodynamic equilibrium and remain in non-equilibrium steady state. Entropy will be transmitted from one subsystem to another, but its production will be zero, which does not contradict the second law of thermodynamics.

In popular culture
In Isaac Asimov's 1956 short story The Last Question, humans repeatedly wonder how the heat death of the universe can be avoided.

In the 1981 Doctor Who story "Logopolis", the Doctor realizes that the Logopolitans have created vents in the universe to expel heat build-up into other universes—"Charged Vacuum Emboitments" or "CVE"—to delay the demise of the universe. The Doctor unwittingly travelled through such a vent in "Full Circle".

In the 1995 computer game I Have No Mouth, and I Must Scream, based on the Harlan Ellison short story of the same name, it is stated that AM, the malevolent supercomputer, will survive the heat death of the universe and continue torturing its immortal victims to eternity.

In the 2011 anime series Puella Magi Madoka Magica, the antagonist Kyubey reveals he is a member of an alien race who has been creating magical girls for millennia in order to harvest their energy to combat entropy and stave off the heat death of the universe.

In the last act of Final Fantasy XIV: Endwalker, the player encounters an alien race known as the Ea who have lost all hope in the future and any desire to live further, all because they have learned of the eventual heat death of the universe and see everything else as pointless due to its probable inevitability.

The overarching plot of the Xeelee Sequence concerns the Photino Birds' efforts to accelerate the heat death of the universe by accelerating the rate at which stars become white dwarves.

The 2019 hit indie video game Outer Wilds has several themes grappling with the idea of the heat death of the universe, and the theory that the universe is a cycle of big bangs once the previous one has experienced a heat death.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Heat death of the universe


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Talk:The Golden Bough

In popular culture section
I see this section has been going and coming a bit lately, but this hasn't been discussed here yet. For what it's worth, my view is that these kinds of sections are rarely of the same standard as the rest of the articles they inhabit, and in this particular case I think it's worth removing altogether. None of the information is sourced, and it simply reads as a list of works which have allegedly been influenced. There's no discussion of any kind, no elaboration and the section is thus out of kilter with the rest of the article. I'd be in favour of keeping it deleted; naturally if there is any WP:RS which discusses the influence of The Golden Bough on popular culture it would be great to mine it for material. Especially if it could be written up in an encyclopaedic way! Kim Dent-Brown  (Talk)  14:28, 18 July 2012 (UTC)

 * I'm not very good with Wikipedia, but the ending of apocalypse now was influenced by it. Francis ford Coppola said that in the director's commentary, and the book in shown in the movie. if anyone would like to add that. Normal Bates (talk) 09:09, 28 August 2022 (UTC)

Overall accuracy of Frazer's thesis
I read English and Ethnology at Edinburgh University in the 90s and I recall Frazer at that time was considered inaccurate, both historically and analytically. No mention of any of that here. Has he been rehabilitated, do you think? — Preceding unsigned comment added by 121.219.176.153 (talk) 12:13, 3 November 2012 (UTC)

 * Yes, in the latter half of the 20th century, his theories were dismissed as inaccurate. But, yes, in recent years, there has been some effort at rehabilitating his ideas, not so much as anthropology, but as philosophical comparative religions.  Some accounting of his reception over many decades, properly cited, would be in order. --- The Old Jacobite The '45  13:38, 3 November 2012 (UTC)

 * His methodology has long been considered quite outdated. Mary Douglas makes a fairly scathing criticism of TGB and Frazer's general approach and theory in the opening chapter or two of Purity and Danger, while also noting the extent to which he mirrors the half-unconscious condescension the Victorians felt for 'the savages'. G.S. Kirk dismisses him as well, after making a thorough check of the "Myth and Ritual" concept which he inspired (the Cambridge school) against the actual record of Greek myths and attested or likely Hellenic rituals (The Nature of Greek Myths, 1975). It's fair to say that at least over the time after Frazer's death in 1941, the influence of TGB on the wider reading public has been *much* greater than its impact on researchers in anthropology, comparative religion or mythology. 83.254.151.33 (talk) 23:54, 8 April 2014 (UTC)

René Girard

 * René Girard is a noted author...and there is no reason his view of Frazer's work should not be represented. The material could perhaps be simplified or improved, but should not be removed outright. It isn't actually "critical reception" of The Golden Bough though, is it? It is instead a micro-summary of a small part of Girard's grand mimetic theory, not well referenced (a single page of The Scapegoat), and potentially WP:OR. It was boldly added, its addition was reverted, and 19 minutes later it was added again without improvement. The material could perhaps be simplified or improved If you are familiar with Girard's mimetic theory, you are welcome to add an improved and/or simplified version of Girard's critical response to Frazer's work, suitably referenced. As the existing paragraph has been rejected twice already by two separate editors, it is verging on lazy scholarship to just reinsert it again, unchanged, and expect others to make it coherent/relevant. Neil S. Walker (talk) 07:59, 20 June 2018 (UTC)

 * The material reads, in part, "Frazer's categorization of scapegoat rituals from across the world is taken up as an important, but incomplete insight by the anthropologist and culture critic René Girard: "By interpreting the expression scapegoat in the ritual sense only and making a generalization of it, Frazer...conceals the most interesting meaning of the expression, which appeared at the beginning of the modern era and which never indicated any kind of rite or theme, or cultural motif, but rather identified the unconscious mechanism for the representation and acts of persecution, the scapegoat mechanism". That certainly seems to be critical reception of The Golden Bough. I do not know why you would suggest otherwise. I also have no idea why you think it might be original research. FreeKnowledgeCreator (talk) 08:01, 20 June 2018 (UTC)

 * Okay, so you're not familiar with The Scapegoat or Girard's mimetic theory. In that case, how about this proposed text?

 * René Girard, a French historian, literary critic, and philosopher of social science, "grudgingly" praised Frazer for recognising kingly sacrifice as "a key primitive ritual", but described his interpretation of the ritual as "a grave injustice to ethnology." Girard's "grievances" against The Golden Bough were numerous, particularly concerning Frazer's assertion that Christianity was merely a perpetuation of primitive myth-ritualism and that the New Testament Gospels were "just further myths of the death and resurrection of the king who embodies the god of vegetation." Girard himself considered the Gospels to be "revelatory texts" rather than myths or the remains of "ignorant superstition", and rejected Frazer's idea that the death of Jesus was a sacrifice, "whatever definition we may give for that sacrifice."

 * Neil S. Walker (talk) 10:54, 20 June 2018 (UTC)

 * Perhaps you should refrain from pointlessly insulting other editors by making baseless presumptions about what they are or are not familiar with? I haven't read The Scapegoat, but I have read some of Girard's other works as well as works about him. There is no logical connection between what I am or am not familiar with and what text you should or should not be proposing for the article. I already noted that I have no objection in principle to having the text about Girard shortened or rewritten. FreeKnowledgeCreator (talk) 11:00, 20 June 2018 (UTC)

 * Well, it's pretty obvious that the text you edit warred to reinsert was less critical response and more a ham-fisted micro-summary of Girard's mimetic theory - which also wrongly implied that Girard was, generally if not entirely, supportive of Frazer's theories presented in TGB. The proposed text addresses these issues. Perhaps you should refrain from edit warring just to make a point. Neil S. Walker (talk) 11:12, 20 June 2018 (UTC)

 * The text in question discusses Frazer. It is not surprising that Girard would discuss Frazer from the perspective of his own theory. I have no objection to your replacing it with your proposed text; I agree that it is an improvement. FreeKnowledgeCreator (talk) 11:15, 20 June 2018 (UTC)

title: Talk:The Golden Bough


text:
Richard Rich, 1st Baron Rich

Richard Rich, 1st Baron Rich (July 1496 – 12 June 1567), was Lord Chancellor during King Edward VI of England's reign, from 1547 until January 1552. He was the founder of Felsted School with its associated almshouses in Essex in 1564. He was a beneficiary of the Dissolution of the Monasteries, and persecuted perceived opponents of the king and their policies. He played a role in the trials of Catholic martyrs Thomas More and John Fisher as well as that of Protestant martyr Anne Askew.

Origins
According to some sources, Rich was born in the London parish of St Lawrence Jewry, the second son of Richard Rich by Joan Dingley, but this is disputed. Also, according to Carter, he was born at Basingstoke, Hampshire, the son of John Rich (d. 1509?), of Penton Mewsey, Hampshire, and a wife named Agnes whose surname is unknown. In 1509, Richard inherited his father's house in Islington, Middlesex. Early in 1551 he was described in an official document as "fifty-four years of age and more", and was therefore born about 1496 or earlier.

According to Sergeaunt (1889): "The origin of the family of Lord Rich has been matter of some discussion ... The first of the family of whom there is definite information was Richard Rich, a wealthy mercer of London and Sheriff of the City in 1441. The date of his death is given by Burke as 1469, but it would seem that he has been confounded with his son John, who was buried in the Mercer’s chapel in that year. The family remained in the city, and the son of John Rich was probably also a mercer. To him was born sometime between 1480 and 1490 a son whom he named Richard."

He had a brother, Robert, whom Henry VIII granted a messuage in Bucklersbury on 24 February 1539, and who died in 1557.

Career
Little is known of Rich's early life. He may have studied at Cambridge before 1516. That year, he entered the Middle Temple as a lawyer and at some point between 1520 and 1525 he was a reader at the New Inn. By 1528 Rich was in search of a patron and wrote to Cardinal Wolsey; in 1529, Thomas Audley succeeded in helping him get elected as an MP for Colchester. As Audley's career advanced in the early 1530s, so did Rich's, through a variety of legal posts, before he became truly prominent in the mid-1530s.

Other preferments followed, and in 1533 Rich was knighted and became the Solicitor General for England and Wales in which capacity he was to act under Thomas Cromwell as a "lesser hammer" for the demolition of the monasteries, and to secure the operation of Henry VIII's Act of Supremacy. Rich had a share in the trials of Thomas More and Bishop John Fisher. In both cases his evidence against the prisoner included admissions made in friendly conversation, and in More's case the words were given a misconstruction that could hardly be other than wilful. While on trial, More said that Rich was "always reputed light of his tongue, a great dicer and gamester, and not of any commendable fame." Rich also played a major part in Cromwell's fall.

As King's Solicitor, Rich travelled to Kimbolton Castle in Huntingdonshire in January 1536 to take the inventory of the goods of Katherine of Aragon, and wrote to Henry advising how he might properly obtain her possessions.

Chancellor
On 19 April 1536 Rich became the chancellor of the Court of Augmentations, established for the disposal of the monastic revenues. His own share of the spoil, acquired either by grant or purchase, included Leez (Leighs) Priory and about 100 manors in Essex. Rich also acquired—and destroyed—the real estate and holdings of the Priory of St Bartholomew-the-Great in Smithfield. He built the Tudor-style gatehouse still surviving in London as the upper portion of the Smithfield Gate. He was Speaker of the House of Commons in the same year, and advocated the king's policy. Despite the share he had taken in the suppression of the monasteries, the prosecution of Thomas More and Bishop Fisher and the part he played under Edward VI and Elizabeth, his religious beliefs remained nominally Catholic.

Rich was also a participant in the torture of Anne Askew, the only woman tortured at the Tower of London. Both he and Chancellor Wriothesley turned the wheels of the rack to torture her.

Baron Rich
Rich was an assistant executor of the will of King Henry VIII, and received a grant of lands. He became Baron Rich of Leez on 26 February 1547. In the next month he succeeded Wriothesley as chancellor. He supported Lord Protector Edward Seymour in his policies, including reforms in Church matters and the prosecution of his brother Thomas Seymour, until the crisis of October 1549, when he joined with John Dudley. He resigned his office in January 1552.

Prosecution of bishops
Rich took part in the prosecution of bishops Stephen Gardiner and Edmund Bonner, and had a role in the harsh treatment accorded to the future Mary I of England. But upon her accession, Mary showed Rich no ill will. He took an active part in the restoration of the old religion in Essex under the new reign, and was one of the most active persecutors. His reappearances in the privy council were rare during Mary's reign, but under Elizabeth he served on a commission to inquire into the grants of land made under Mary, and in 1566 was sent for to advise on the question of the queen's marriage. He died at Rochford in Essex, on 12 June 1567, and was buried in Holy Cross Church in Felsted.

In Mary's reign he founded a chaplaincy with provision for the singing of masses and dirges, and the ringing of bells in Felsted church. To this was added a Lenten allowance of herrings to the inhabitants of three parishes. These donations were transferred in 1564 to the foundation of Felsted School for instruction, primarily for children born on the founder's manors, in Latin, Greek, and divinity. The patronage of the school remained in the founder's family until 1851.

Descendants
Rich's descendants formed the powerful Rich family, lasting for three centuries, acquiring several titles in the Peerage of England and intermarrying with numerous other noble families.

By his wife Elizabeth Jenks (Gynkes) (d.1558) he had 15 children. Thirteen of them are shown in the Essex pedigrees. The eldest son, Robert (1537?–1581), second Baron Rich, supported the Reformation.

One grandson, Richard Rich, was the first husband of Katherine Knyvet: another, the younger Robert Rich, third Baron Rich (1559–1619) was created First Earl of Warwick (of the third creation) in 1618, and was the father of Robert Rich, 2nd Earl of Warwick, who was Commander of the Commonwealth Navy during the Interregnum. This line failed with the death of the 8th Earl on 7 September 1759.

Rich had an illegitimate son named Richard (d. 1598 ) whom he acknowledged fully in his will with legacies and guardians for his minority, his education in the common law, and suitable marital arrangements. In this line of descent was his grandson the merchant adventurer Sir Nathaniel Rich, and his great-grandson Nathaniel Rich (nephew of the elder Nathaniel), a colonel in the New Model Army during the English Civil War.

Legacy
Since the mid-16th century Rich has had a reputation for immorality, financial dishonesty, double-dealing, perjury and treachery rarely matched in English history. The historian Hugh Trevor-Roper called Rich a man "of whom nobody has ever spoken a good word".

Depiction in the arts
Rich is the supporting villain in the play A Man for All Seasons by Robert Bolt, which shows his slide into corruption. In the subsequent, Oscar-winning film adaptation, John Hurt portrays him. Bolt depicts Rich as perjuring himself against More in order to become Attorney-General for Wales. More responds, "Why, Richard, it profits a man nothing to give his soul for the whole world...but for Wales?" The final line of the film notes that Rich "died in his bed" in juxtaposition with More's martyrdom and the other major characters' untimely deaths. In the 1988 remake of the film, Jonathan Hackett portrayed Rich.

Rich is a supporting character in C. J. Sansom's Shardlake series of historical mystery novels, which are set in Henry VIII's reign. Rich is portrayed as a cruel villain who is prepared to subvert justice to enhance his property and position. He has a significant role in the plot of Sovereign, the third of the series, and in Heartstone, the fifth.

Rod Hallett played Rich in seasons two, three and four of the Showtime series The Tudors.

Rich (spelled Riche in the novels) appears in Hilary Mantel's three volumes about Thomas Cromwell, Wolf Hall, Bring Up the Bodies and The Mirror and the Light. Bryan Dick portrays him in the BBC television adaptation of the first two novels, Wolf Hall.

title: Richard Rich, 1st Baron Rich


text:
Negative temperature

Certain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system. A standard example of such a system is population inversion in laser physics.

Thermodynamic systems with unbounded phase space cannot achieve negative temperatures: adding heat always increases their entropy. The possibility of a decrease in entropy as energy increases requires the system to "saturate" in entropy. This is only possible if the number of high energy states is limited. For a system of ordinary (quantum or classical) particles such as atoms or dust, the number of high energy states is unlimited (particle momenta can in principle be increased indefinitely). Some systems, however (see the examples below), have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.

History
The possibility of negative temperatures was first predicted by Lars Onsager in 1949. Onsager was investigating 2D vortices confined within a finite area, and realized that since their positions are not independent degrees of freedom from their momenta, the resulting phase space must also be bounded by the finite area. Bounded phase space is the essential property that allows for negative temperatures, and can occur in both classical and quantum systems. As shown by Onsager, a system with bounded phase space necessarily has a peak in the entropy as energy is increased. For energies exceeding the value where the peak occurs, the entropy decreases as energy increases, and high-energy states necessarily have negative Boltzmann temperature.

The limited range of states accessible to a system with negative temperature means that negative temperature is associated with emergent ordering of the system at high energies. For example in Onsager's point-vortex analysis negative temperature is associated with the emergence of large-scale clusters of vortices. This spontaneous ordering in equilibrium statistical mechanics goes against common physical intuition that increased energy leads to increased disorder.

It seems negative temperatures were first found experimentally in 1951, when Purcell and Pound observed evidence for them in the nuclear spins of a lithium fluoride crystal placed in a magnetic field, and then removed from this field. They wrote:

 * A system in a negative temperature state is not cold, but very hot, giving up energy to any system at positive temperature put into contact with it. It decays to a normal state through infinite temperature.

Definition of temperature
The absolute temperature (Kelvin) scale can be loosely interpreted as the average kinetic energy of the system's particles. The existence of negative temperature, let alone negative temperature representing "hotter" systems than positive temperature, would seem paradoxical in this interpretation. The paradox is resolved by considering the more rigorous definition of thermodynamic temperature in terms of Boltzmann's entropy formula. This reveals the tradeoff between internal energy and entropy contained in the system, with "coldness", the reciprocal of temperature, being the more fundamental quantity. Systems with a positive temperature will increase in entropy as one adds energy to the system, while systems with a negative temperature will decrease in entropy as one adds energy to the system.

The definition of thermodynamic temperature $T$ is a function of the change in the system's entropy $S$  under reversible heat transfer $Q_{rev}$:
 * $$T = \frac{dQ_\mathrm{rev}}{dS}.$$

Entropy being a state function, the integral of $dS$ over any cyclical process is zero. For a system in which the entropy is purely a function of the system's energy $E$, the temperature can be defined as:
 * $$ T = \left( \frac{dS}{dE} \right)^{-1}.$$

Equivalently, thermodynamic beta, or "coldness", is defined as
 * $$\beta = \frac{1}{kT} = \frac{1}{k} \frac{dS}{dE},$$

where $k$ is the Boltzmann constant.

Note that in classical thermodynamics, $S$ is defined in terms of temperature. This is reversed here, $S$ is the statistical entropy, a function of the possible microstates of the system, and temperature conveys information on the distribution of energy levels among the possible microstates. For systems with many degrees of freedom, the statistical and thermodynamic definitions of entropy are generally consistent with each other.

Some theorists have proposed using an alternative definition of entropy as a way to resolve perceived inconsistencies between statistical and thermodynamic entropy for small systems and systems where the number of states decreases with energy, and the temperatures derived from these entropies are different. It has been argued that the new definition would create other inconsistencies; its proponents have argued that this is only apparent.

Heat and molecular energy distribution
Negative temperatures can only exist in a system where there are a limited number of energy states (see below). As the temperature is increased on such a system, particles move into higher and higher energy states, and as the temperature increases, the number of particles in the lower energy states and in the higher energy states approaches equality. (This is a consequence of the definition of temperature in statistical mechanics for systems with limited states.) By injecting energy into these systems in the right fashion, it is possible to create a system in which there are more particles in the higher energy states than in the lower ones. The system can then be characterised as having a negative temperature.

A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it,

"The temperature scale from cold to hot runs:"

The corresponding inverse temperature scale, for the quantity $β = 1⁄kT$ (where $k$ is the Boltzmann constant), runs continuously from low energy to high as +∞, …, 0, …, −∞. Because it avoids the abrupt jump from +∞ to −∞, $β$ is considered more natural than $T$. Although a system can have multiple negative temperature regions and thus have −∞ to +∞ discontinuities.

In many familiar physical systems, temperature is associated to the kinetic energy of atoms. Since there is no upper bound on the momentum of an atom, there is no upper bound to the number of energy states available when more energy is added, and therefore no way to get to a negative temperature. However, in statistical mechanics, temperature can correspond to other degrees of freedom than just kinetic energy (see below).

Temperature and disorder
The distribution of energy among the various translational, vibrational, rotational, electronic, and nuclear modes of a system determines the macroscopic temperature. In a "normal" system, thermal energy is constantly being exchanged between the various modes.

However, in some situations, it is possible to isolate one or more of the modes. In practice, the isolated modes still exchange energy with the other modes, but the time scale of this exchange is much slower than for the exchanges within the isolated mode. One example is the case of nuclear spins in a strong external magnetic field. In this case, energy flows fairly rapidly among the spin states of interacting atoms, but energy transfer between the nuclear spins and other modes is relatively slow. Since the energy flow is predominantly within the spin system, it makes sense to think of a spin temperature that is distinct from the temperature associated to other modes.

A definition of temperature can be based on the relationship:

 * $$T = \frac{dq_\mathrm{rev}}{dS}$$

The relationship suggests that a positive temperature corresponds to the condition where entropy, $S$, increases as thermal energy, $q_{rev}$, is added to the system. This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and non-spin-related electronic and nuclear modes. The reason for this is that there are an infinite number of these types of modes, and adding more heat to the system increases the number of modes that are energetically accessible, and thus increases the entropy.

Noninteracting two-level particles
The simplest example, albeit a rather nonphysical one, is to consider a system of $N$ particles, each of which can take an energy of either $+ε$ or $−ε$ but are otherwise noninteracting. This can be understood as a limit of the Ising model in which the interaction term becomes negligible. The total energy of the system is

 * $$E = \varepsilon\sum_{i=1}^N \sigma_i = \varepsilon j$$

where $N$ is the sign of the $σ_{i}$th particle and $i$ is the number of particles with positive energy minus the number of particles with negative energy. From elementary combinatorics, the total number of microstates with this amount of energy is a binomial coefficient:

 * $$\Omega_E = \binom{N}\frac{N + j}{2} = \frac{N!}{\left(\frac{N + j}{2}\right)! \left(\frac{N - j}{2}\right)!}.$$

By the fundamental assumption of statistical mechanics, the entropy of this microcanonical ensemble is

 * $$S = k_\text{B} \ln \Omega_E$$

We can solve for thermodynamic beta ($β = 1⁄k_{B}T$) by considering it as a central difference without taking the continuum limit:

 * $$\begin{align}

\beta &= \frac{1}{k_\mathrm{B}} \frac{\delta_{2\varepsilon}[S]}{2\varepsilon}\\[3pt] &= \frac{1}{2\varepsilon} \left( \ln \Omega_{E+\varepsilon} - \ln \Omega_{E-\varepsilon} \right)\\[3pt] &= \frac{1}{2\varepsilon} \ln \left( \frac{\left(\frac{N + j - 1}{2}\right)! \left(\frac{N - j + 1}{2}\right)!}{\left(\frac{N + j + 1}{2}\right)! \left(\frac{N - j - 1}{2}\right)!} \right)\\[3pt] &= \frac{1}{2\varepsilon} \ln \left( \frac{N - j + 1}{N + j + 1} \right). \end{align}$$

hence the temperature

 * $$T(E) = \frac{2\varepsilon}{k_\text{B}}\left[\ln \left( \frac{(N + 1)\varepsilon - E}{(N + 1)\varepsilon + E} \right)\right]^{-1}.$$

This entire proof assumes the microcanonical ensemble with energy fixed and temperature being the emergent property. In the canonical ensemble, the temperature is fixed and energy is the emergent property. This leads to ($j$ refers to microstates):
 * $$\begin{align}

Z(T) &= \sum_{i=1}^N e^{-\varepsilon_i\beta}\\[6pt] E(T) &= \frac{1}{Z}\sum_{i=1}^N \varepsilon_i e^{-\varepsilon_i\beta}\\[6pt] S(T) &= k_\text{B}\ln(Z) + \frac{E}{T} \end{align}$$

Following the previous example, we choose a state with two levels and two particles. This leads to microstates $ε_{1} = 0$, $ε_{2} = 1$, $ε_{3} = 1$, and $ε_{4} = 2$.
 * $$\begin{align}

Z(T) &= e^{-0\beta} + 2e^{-1\beta} + e^{-2\beta}\\[3pt] &= 1 + 2e^{-\beta} + e^{-2\beta}\\[6pt] E(T) &= \frac{0e^{-0\beta} + 2 \times 1e^{-1\beta} + 2e^{-2\beta}}{Z}\\[3pt] &= \frac{2e^{-\beta} + 2e^{-2\beta}}{Z}\\[3pt] &= \frac{2e^{-\beta} + 2e^{-2\beta}}{1 + 2e^{-\beta} + e^{-2\beta}}\\[6pt] S(T) &= k_\text{B}\ln\left(1 + 2e^{-\beta} + e^{-2\beta}\right) + \frac{2e^{-\beta} + 2e^{-2\beta}}{\left(1 + 2e^{-\beta} + e^{-2\beta}\right)T} \end{align}$$

The resulting values for $ε$, $S$, and $E$ all increase with $Z$ and never need to enter a negative temperature regime.

Nuclear spins
The previous example is approximately realized by a system of nuclear spins in an external magnetic field. This allows the experiment to be run as a variation of nuclear magnetic resonance spectroscopy. In the case of electronic and nuclear spin systems, there are only a finite number of modes available, often just two, corresponding to spin up and spin down. In the absence of a magnetic field, these spin states are degenerate, meaning that they correspond to the same energy. When an external magnetic field is applied, the energy levels are split, since those spin states that are aligned with the magnetic field will have a different energy from those that are anti-parallel to it.

In the absence of a magnetic field, such a two-spin system would have maximum entropy when half the atoms are in the spin-up state and half are in the spin-down state, and so one would expect to find the system with close to an equal distribution of spins. Upon application of a magnetic field, some of the atoms will tend to align so as to minimize the energy of the system, thus slightly more atoms should be in the lower-energy state (for the purposes of this example we will assume the spin-down state is the lower-energy state). It is possible to add energy to the spin system using radio frequency techniques. This causes atoms to flip from spin-down to spin-up.

Since we started with over half the atoms in the spin-down state, this initially drives the system towards a 50/50 mixture, so the entropy is increasing, corresponding to a positive temperature. However, at some point, more than half of the spins are in the spin-up position. In this case, adding additional energy reduces the entropy, since it moves the system further from a 50/50 mixture. This reduction in entropy with the addition of energy corresponds to a negative temperature. In NMR spectroscopy, this corresponds to pulses with a pulse width of over 180° (for a given spin). While relaxation is fast in solids, it can take several seconds in solutions and even longer in gases and in ultracold systems; several hours were reported for silver and rhodium at picokelvin temperatures. It is still important to understand that the temperature is negative only with respect to nuclear spins. Other degrees of freedom, such as molecular vibrational, electronic and electron spin levels are at a positive temperature, so the object still has positive sensible heat. Relaxation actually happens by exchange of energy between the nuclear spin states and other states (e.g. through the nuclear Overhauser effect with other spins).

Lasers
This phenomenon can also be observed in many lasing systems, wherein a large fraction of the system's atoms (for chemical and gas lasers) or electrons (in semiconductor lasers) are in excited states. This is referred to as a population inversion.

The Hamiltonian for a single mode of a luminescent radiation field at frequency $T$ is
 * $$H = (h\nu - \mu)a^\dagger a.$$

The density operator in the grand canonical ensemble is
 * $$\rho = \frac{e^{-\beta H}}{\operatorname{Tr}\left(e^{-\beta H}\right)}.$$

For the system to have a ground state, the trace to converge, and the density operator to be generally meaningful, $βH$ must be positive semidefinite. So if $hν < μ$, and $ν$ is negative semidefinite, then $H$ must itself be negative, implying a negative temperature.

Motional degrees of freedom
Negative temperatures have also been achieved in motional degrees of freedom. Using an optical lattice, upper bounds were placed on the kinetic energy, interaction energy and potential energy of cold potassium-39 atoms. This was done by tuning the interactions of the atoms from repulsive to attractive using a Feshbach resonance and changing the overall harmonic potential from trapping to anti-trapping, thus transforming the Bose-Hubbard Hamiltonian from $Ĥ → −Ĥ$. Performing this transformation adiabatically while keeping the atoms in the Mott insulator regime, it is possible to go from a low entropy positive temperature state to a low entropy negative temperature state. In the negative temperature state, the atoms macroscopically occupy the maximum momentum state of the lattice. The negative temperature ensembles equilibrated and showed long lifetimes in an anti-trapping harmonic potential.

Two-dimensional vortex motion
The two-dimensional systems of vortices confined to a finite area can form thermal equilibrium states at negative temperature, and indeed negative temperature states were first predicted by Onsager in his analysis of classical point vortices. Onsager's prediction was confirmed experimentally for a system of quantum vortices in a Bose-Einstein condensate in 2019.

title: Negative temperature


text:
Heat death

Heat death may refer to:

 * Heat death of the universe, a proposed cosmological event
 * Heat death paradox, a philosophical examination of the cosmological event
 * Hyperthermia, injury up to and including death, from excessive heat
 * Thermal shock, the destruction of equipment by overheating

In arts

 * The Heat Death of the Universe, 2003 album by punk band Off Minor
 * "The Heat Death of the Universe", a short story by Pamela Zoline

title: Heat death