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Donnybrook, Dublin

Donnybrook is a district of Dublin, Ireland, on the southside of the city, in the Dublin 4 postal district. It is home to the Irish public service broadcaster Raidió Teilifís Éireann (RTÉ) and was once part of the Pembroke Township. Its neighbouring suburbs are Ballsbridge, Sandymount, Ranelagh and Clonskeagh.

Donnybrook is also a civil parish mainly situated in the old barony of Dublin.

History
Donnybrook Fair dates from a charter of King John of England in 1204 and was held annually until 1855. It began as a fair for livestock and agricultural produce but later declined, growing into more of a carnival and funfair. Drunkenness, fighting, and hasty marriages became commonplace and the people of Donnybrook were anxious that it should cease. Eventually, the fair's reputation for tumult was its undoing. From the 1790s on, there were campaigns against the drunken brawl the fair had become. After a good deal of local fundraising, the patent was bought by a group of prominent residents and clergy, bringing about its demise. The Fair took place on lands now occupied by Donnybrook Rugby Ground and the Ever Ready Garage. The word donnybrook has since entered the English language to describe a rowdy brawl.

Donnybrook castle
Donnybrook Castle was an Elizabethan mansion and residence of the Ussher family. James Ussher was appointed Archbishop of Armagh in the Church of Ireland by Queen Elizabeth I of England. The mansion was demolished in 1759 and later replaced in 1795 by the existing Georgian house. It is now occupied by the Religious Sisters of Charity.

Donnybrook cemetery
Donnybrook Cemetery dates back to the 8th century and was once the location of a church founded by St Broc. It was also the site of Catholic and Church of Ireland churches, both called St Mary's. Those buried in it include Dr Bartholomew Mosse, the founder of the Rotunda Hospital, Sir Edward Lovett Pearce, architect of the Irish Houses of Parliament on College Green and Dr Richard Madden, biographer of the United Irishmen. It is possible that the wall on the south side of the cemetery is the oldest man-made structure still existing in Donnybrook. The brick chimney behind the cemetery was built on the site of a former marble works and later served as a Magdalene laundry. Two ancestors of Meghan Markle, Mary McCue and Thomas Bird, an English soldier, were married at St Mary's Church of Ireland church, Donnybrook, in 1860.

Geography
The river Dodder runs through Donnybrook and at one time there was a ford here. It is subject to periodic serious flooding and in 1628 one of the Usshers of Donnybrook Castle drowned while trying to cross.

Civil parish
Donnybrook is a civil parish consisting of sixteen townlands. All but four of these townlands are situated in the Barony of Dublin. Donnybrook is the single biggest parish in that barony. The most southerly townlands, Annefield, Simmonscourt and Priesthouse, belong to the barony of Rathdown. The smallest of these, Annefield, is itself an enclave of Simmonscourt which gives its name to a pavilion of the Royal Dublin Society. Today, the majority of Priesthouse is occupied by Elm Park Golf Club and the studios of RTÉ. The remaining townland of Sallymount - the parish's most westerly point - is in the barony of Uppercross.

Donnybrook today
The television and radio studios of the national broadcaster, RTÉ, are located in Priesthouse, Donnybrook. There is also a large Dublin Bus garage located in the area.

Politics
Donnybrook is in the Dáil Éireann constituency of Dublin Bay South and the Pembroke local electoral area of Dublin City Council.

Education

 * Donnybrook is home to the all-girls Muckross Park College.
 * St. Mary's mixed primary school is located on Belmont Avenue.
 * The Teresian School is an all-girls Secondary, Junior and Pre-School in Stillorgan Rd.

People

 * Writers
 * Patrick Kavanagh
 * Anthony Trollope
 * Flann O'Brien aka Myles na gCopaleen aka Brian O'Nolan, lived on Belmont Avenue
 * Benedict Kiely
 * Padraic Colum
 * Brendan Behan
 * Denis Johnston and his wife, the actress/director Shelah Richards

 * Others
 * Jack B. Yeats
 * Sir Ernest Henry Shackleton
 * John Boyd Dunlop (pneumatic tyre inventor)
 * Guglielmo Marconi (wireless radio - lived in Montrose House, the family home of his mother's family the Jamesons of whiskey fame, now on the grounds of the national broadcaster RTÉ)
 * Éamon de Valera (President of Ireland)
 * Pádraig Pearse (a leader of the 1916 Easter Rising)
 * The O'Rahilly (also a senior figure in the 1916 Easter Rising)
 * Michael Collins (Chairman of the Provisional Government and commander-in-chief of the National Army. killed during the Irish Civil War in 1922)
 * George E. H. McElroy (WWI fighter ace RFC/RAF)
 * Garret FitzGerald (former Taoiseach of Ireland)
 * Albert Reynolds (former Taoiseach of Ireland)
 * Shane MacGowan (singer/lyricist for the Pogues)
 * Méav Ní Mhaolchatha (Singer, former Celtic Woman)
 * Frederick May
 * William Downes, 1st Baron Downes (eminent nineteenth-century judge)
 * Richard Gibson - Actor - Played part of Herr Otto Flick in sitcom series 'Allo 'Allo!
 * Beatrice Doran, librarian, historian, and author

Sport
Donnybrook is the traditional home of rugby union in Leinster. The headquarters of the Irish Rugby Football Union Leinster Branch is located opposite Donnybrook Stadium, where the professional Leinster team played their home games until recently. Most games are hosted in Donnybrook Stadium. Some Junior Cup ties are also hosted on the grounds.

Rugby clubs Bective Rangers and Old Wesley have their home ground in Donnybrook Stadium. During the school year secondary schools such as St Conleth's College, Blackrock, Belvedere College, Wesley College, Clongowes, St. Michaels and many more play rugby in Donnybrook Stadium.

There are several tennis clubs in Donnybrook, Donnybrook Lawn Tennis Club (LTC), St.Marys LTC and Bective LTC.

Belmont Football Club has its home ground in Herbert Park.

Merrion Cricket Club is located in Donnybrook, off Anglesea Road and backing onto the Dodder.

title: Donnybrook, Dublin


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Ballsbridge

Ballsbridge (from historic Ball's Bridge) is an affluent neighbourhood of the city of Dublin, the capital of Ireland. The area is largely situated north and west of a three-arch stone bridge across the River Dodder, on the south side of the city. The sign on the bridge still proclaims it as "Ball's Bridge", in recognition of the fact that the original bridge on that location was built and owned by the Ball family, a well-known Dublin merchant family in the 1500s and the 1600s. The current bridge was built in 1791.

Ballsbridge was once part of the Pembroke Township.

History
18th-century maps show that the area of Dublin that is now Ballsbridge was originally mud flats and marsh, with many roads converging on a small village located around the bridge, and known already as Ballsbridge. Situated on the Dodder, this village had a ready source of power for small industries, including by the 1720s, a linen and cotton printers, and, by the 1750s, a paper mill and a gunpowder factory.

The land around Ballsbridge was rural and mostly belonged to the Earl of Pembroke. After the Royal Dublin Society (RDS) moved into its present site near Ballsbridge in 1879, the Earl of Pembroke began to develop these lands into suburban residential housing. The RDS held their first show on their new premises in the early 1880s. In 1903, the land formerly known as the 'Forty Acres' was given to the city by the Earl of Pembroke to establish Herbert Park.(The Earl of Pembroke's surname was Herbert.)

Until 1965, there was a well-known botanical garden on Landsdowne Road near Ballsbridge. The garden belonged to Trinity College, which had leased land from the Earl of Pembroke. In 1960, the original lease from the Pembroke Estate expired and was not renewed. After reducing their size considerably, Trinity decided, in 1965, to close the botanical gardens at that location and to open a new garden at Dartry. Two hotels now stand on the site.

In 1916, the Mount Street bridge, which spans the Grand Canal at the foot of Northumberland Road, was the site of an important battle during the Easter Rising. The O'Rahilly, one of the leaders of the Rising, lived at 40 Herbert Park. Another resistance leader, Eoin MacNeill, who refused to participate in the Rising, lived down the road at 19 Herbert Park.

Popular culture
The date of 16 June 1904, now commemorated as Bloomsday, was chosen by the writer James Joyce for the setting of his novel Ulysses because it was the date on which he lost his virginity to his girlfriend Nora Barnacle - Joyce was renting a room at the time in a house at 60 Shelbourne Road.

In the 1940s and 50s, the writer Brendan Behan lived in Ballsbridge, as did the poet Patrick Kavanagh, who lived at 62 Pembroke Road. Busts of Behan and Kavanagh are on display at two pubs along Pembroke Road, Searson's and the Wellington. Kavanagh wrote his famous poem On Raglan Road about a girl he met on that street in 1944.

Buildings, structures and parks
The bridge itself forms the heart of the Ballsbridge suburb which extends northwards towards the Grand Canal along Northumberland Road up to Haddington Road and Shelbourne Road, southwards along the Merrion Road towards Merrion and along Anglesea Road towards Donnybrook, and westwards to encompass the area around Pembroke Road, Clyde Road, Elgin Road and Herbert Park. The bridge was extensively modernised and widened by 24 feet in 1900 by William Kaye-Parry.

Herbert Park, a public park, is thirty-two acres in size and is divided by a road, also called Herbert Park, and forms part of Ballsbridge's nebulous border with Donnybrook.

The Royal Dublin Society (RDS) has its grounds here, and the Lansdowne Road headquarters of the Irish Rugby Football Union (IRFU) is on the boundary between Ballsbridge and Irishtown. The corporate headquarters of Allied Irish Banks (AIB) are also located in Ballsbridge. The former Pembroke Town Hall is located to the immediate northwest of the RDS. Ailesbury Road, along with adjacent Shrewsbury Road, contains the most expensive properties in Dublin, and the roads are featured in the Irish edition of the board game Monopoly. Shrewsbury Road was the sixth most expensive street in the world in 2007.

Many of Dublin's embassies and diplomatic residences are located in the southern part of Ballsbridge on and around Ailesbury Road. The British, American, Italian, Spanish, Dutch and Israeli embassies are all located in the Ballsbridge area of Dublin.

The U.S. embassy, an iconic cylindrical building, is a major landmark in present-day Ballsbridge. It was designed in 1955 by John M. Johansen, Professor of Architecture at Yale University. The project was 9 years in incubation and the building was inaugurated in 1964.

Gurdwara Guru Nanak Darbar, the place of assembly and worship for the Irish Sikh community, is located on Serpentine Avenue. It is located on the site of the old Oscar Cinema which the community purchased in 1987.

Transport
The DART train passes nearby, stopping at Lansdowne Road (which is also frequently served by commuter services) and Sandymount stations.

Ballsbridge used to be served by the Dublin tramways 6, 7 and 8, and also served as the terminus for tram line 5 back when Ballsbridge was still known as Pembroke. The tram lines were closed throughout the 1930s and 1940s and the 6, 7 and 8 were the last to close, with all three ending on 9 July 1949.

Ballsbridge is serviced by the following bus routes:
 * 4 Ballymun to Monkstown
 * 7 Cherrywood to Dublin
 * 7a Loughlinstown to Dublin
 * 18 Palmerstown to Sandymount
 * 27X Clare Hall to Belfield

A number of services have been withdrawn due to Dublin Bus' Network Direct route restructuring programme.

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

title: Ballsbridge


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IS-IS

Intermediate System to Intermediate System  (IS-IS, also written ISIS) is a routing protocol designed to move information efficiently within a computer network, a group of physically connected computers or similar devices. It accomplishes this by determining the best route for data through a packet switching network.

The IS-IS protocol is defined in ISO/IEC 10589:2002 as an international standard within the Open Systems Interconnection (OSI) reference design. The Internet Engineering Task Force (IETF) republished IS-IS in, but that RFC was later marked as historic by because it republished a draft rather than a final version of the (International Organization for Standardization) ISO standard, causing confusion.

In 2005, IS-IS was called "the de facto standard for large service provider network backbones."

Description
IS-IS is an interior gateway protocol, designed for use within an administrative domain or network. This is in contrast to exterior gateway protocols, primarily Border Gateway Protocol (BGP), which is used for routing between autonomous systems (RFC 1930).

IS-IS is a link-state routing protocol, operating by reliably flooding link state information throughout a network of routers. Each IS-IS router independently builds a database of the network's topology, aggregating the flooded network information. Like the OSPF protocol, IS-IS uses Dijkstra's algorithm for computing the best path through the network. Packets (datagrams) are then forwarded, based on the computed ideal path, through the network to the destination.

History
The IS-IS protocol was developed by a team of people working at Digital Equipment Corporation as part of DECnet Phase V. It was standardized by the ISO in 1992 as ISO 10589 for communication between network devices that are termed Intermediate Systems (as opposed to end systems or hosts) by the ISO. The purpose of IS-IS was to make the routing of datagrams possible using the ISO-developed OSI protocol stack called CLNS.

IS-IS was developed at roughly the same time that the Internet Engineering Task Force IETF was developing a similar protocol called OSPF. IS-IS was later extended to support routing of datagrams in the Internet Protocol (IP), the network-layer protocol of the global Internet. This version of the IS-IS routing protocol was then called Integrated IS-IS (RFC 1195)

Packet types
IS-IS adjacency can be either broadcast or point-to-point.

 * IS-IS Hello PDU (IIH)
 * The IS-IS hello packets needs to be exchanged periodically between 2 routers to establish adjacency. Based on the negotiation, one of them will be selected as DIS (Designated IS). This hello packet will be sent separately for Level-1 or Level-2.

 * Link State PDU (LSP)
 * This contains the actual route information. This LSP can contain many type–length–values (TLVs).

 * Complete Sequence Number PDU (CSNP)
 * This packet will be sent only by the DIS. By default for every 10 seconds, CSNP packet will be transmitted by DIS. This will contain the list of LSP IDs along with sequence number and checksum.

 * Partial Sequence Number PDU (PSNP)
 * If the router which receives CSNP packet finds some discrepancy in its own database, it will send an PSNP request asking the DIS to send specific LSP back to it.

Other uses
IS-IS is also used as the control plane for IEEE 802.1aq Shortest Path Bridging (SPB). SPB allows for shortest-path forwarding in an Ethernet mesh network context utilizing multiple equal cost paths. This permits SPB to support large Layer 2 topologies, with fast convergence, and improved use of the mesh topology. Combined with this is single point provisioning for logical connectivity membership. IS-IS is therefore augmented with a small number of TLVs and sub-TLVs, and supports two Ethernet encapsulating data paths, 802.1ad Provider Bridges and 802.1ah Provider Backbone Bridges. SPB requires no state machine or other substantive changes to IS-IS, and simply requires a new Network Layer Protocol Identifier (NLPID) and set of TLVs. This extension to IS-IS is defined in the IETF proposed standard RFC 6329.

Related protocols

 * Fabric Shortest Path First (FSPF)
 * Transparent Interconnect of Lots of Links (TRILL)

title: IS-IS


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Amaterasu

Amaterasu Ōmikami (天照大御神, 天照大神), often called Amaterasu for short, also known as Ōhirume no Muchi no Kami (大日孁貴神), is the goddess of the sun in Japanese mythology. Often considered the chief deity (kami) of the Shinto pantheon,  she is also portrayed in Japan's earliest literary texts, the Kojiki (c. 712 CE) and the Nihon Shoki (720 CE), as the ruler (or one of the rulers) of the heavenly realm Takamagahara and the mythical ancestress of the Imperial House of Japan via her grandson Ninigi. Along with her siblings, the moon deity Tsukuyomi and the impetuous storm god Susanoo, she is considered to be one of the "Three Precious Children" (三貴子, ), the three most important offspring of the creator god Izanagi.

Amaterasu’s chief place of worship, the Grand Shrine of Ise in Ise, Mie Prefecture, is one of Shinto's holiest sites and a major pilgrimage center and tourist spot. As with other Shinto kami, she is also enshrined in a number of Shinto shrines throughout Japan.

Name
The goddess is referred to as 'Amaterasu Ōmikami' (天照大御神 / 天照大神; historical orthography: あまてらすおほみかみ, Amaterasu Ohomikami; Old Japanese: Amaterasu Opomi1kami2) in the Kojiki, while the Nihon Shoki gives the following variant names:

 * Ōhirume-no-Muchi (大日孁貴; Man'yōgana: 於保比屢咩能武智; hist. orthography: おほひるめのむち, Ohohirume-no-Muchi; Old Japanese: Opopi1rume1-no2-Muti)
 * Amaterasu Ō(mi)kami (天照大神; hist. orthography: あまてらすおほ(み)かみ, Amaterasu Oho(mi)kami)
 * Amaterasu Ōhirume no Mikoto (天照大日孁尊)
 * Hi-no-Kami (日神; OJ: Pi1-no-Kami2)

'Amaterasu' is thought to derive from the verb amateru "to illuminate / shine in the sky" (ama "sky, heaven" + teru "to shine") combined with the honorific auxiliary verb -su, while 'Ōmikami' means "great august deity" (ō "great" + honorific prefix mi- + kami). Notably, 'Amaterasu' in 'Amaterasu Ōmikami' is not technically a name the same way 'Susanoo' in 'Susa no O no Mikoto' or 'Ōkuninushi' in 'Ōkuninushi no Kami' are. Amaterasu is an attributive verb form that modifies the noun after it, ōmikami. This epithet is therefore, much more semantically transparent than most names recorded in the Kojiki and Nihon Shoki, in that it means exactly what it means, without allusion, inference or etymological opacity, literally "The Great August Goddess Who Shines in Heaven". This usage is analogous to the use of relative clauses in English, only different in that Japanese clauses are placed in front of the noun they modify. This is further exemplified by (1) an alternative epithet, 'Amateru Kami' (天照神, "The Goddess Who Shines in Heaven"), which is a plain, non-honorific version of 'Amaterasu Ōmikami', (2) alternative forms of the verb amaterasu used elsewhere, for example its continuative form amaterashi (天照之) in the Nihon Sandai Jitsuroku, and (3) similar uses of attributive verb forms in certain epithets, such as Emperor Jinmu's Hatsu Kunishirasu Sumeramikoto (始馭天下之天皇, "His Majesty Who First Rules the Land"). There are, still, certain verb forms that are treated as proper names, such as the terminal negative fukiaezu in 'Ugayafukiaezu no Mikoto' (鸕鷀草葺不合尊, "His Augustness, Incompletely-Thatched-with-Comoran-Feathers")

Her other name, 'Ōhirume', is usually understood as meaning "great woman of the sun / daytime" (cf. hiru "day(time), noon", from hi "sun, day" + me "woman, lady"), though alternative etymologies such as "great spirit woman" (taking hi to mean "spirit") or "wife of the sun" (suggested by Orikuchi Shinobu, who put forward the theory that Amaterasu was originally conceived of as the consort or priestess of a male solar deity) had been proposed. A possible connection with the name Hiruko (the child rejected by the gods Izanagi and Izanami and one of Amaterasu's siblings) has also been suggested. To this name is appended the honorific muchi, which is also seen in a few other theonyms such as 'Ō(a)namuchi' or 'Michinushi-no-Muchi' (an epithet of the three Munakata goddesses ).

As the ancestress of the imperial line, the epithet 'Sume(ra)-Ō(mi)kami' (皇大神, lit. "great imperial deity"; also read as 'Kōtaijin' ) is also applied to Amaterasu in names such as 'Amaterasu Sume(ra) Ō(mi)kami' (天照皇大神, also read as 'Tenshō Kōtaijin') and 'Amaterashimasu-Sume(ra)-Ōmikami' (天照坐皇大御神).

During the medieval and early modern periods, the deity was also referred to as 'Tenshō Daijin' (the on'yomi of 天照大神) or 'Amateru Ongami' (an alternate reading of the same).

The name 'Amaterasu Ōmikami' has been translated into English in different ways. While a number of authors such as Donald Philippi rendered it as "heaven-illuminating great deity," Basil Hall Chamberlain argued (citing the authority of Motoori Norinaga) that it is more accurately understood to mean "shining in heaven" (because the auxiliary su is merely honorific, not causative, such interpretation as "to make heaven shine" would miss the mark), and accordingly translated it as "Heaven-Shining-Great-August-Deity". Gustav Heldt's 2014 translation of the Kojiki, meanwhile, renders it as "the great and mighty spirit Heaven Shining."

Birth
Both the Kojiki (c. 712 CE) and the Nihon Shoki (720 CE) agree in their description of Amaterasu as the daughter of the god Izanagi and the elder sister of Tsukuyomi, the deity of the moon, and Susanoo, the god of storms and seas. The circumstances surrounding the birth of these three deities, known as the "Three Precious Children" (三貴子, mihashira no uzu no miko or sankishi), however, vary between sources:

 * In the Kojiki, Amaterasu, Tsukuyomi and Susanoo were born when Izanagi went to "[the plain of] Awagihara by the river-mouth of Tachibana in Himuka in [the island of] Tsukushi" and bathed (misogi) in the river to purify himself after visiting Yomi, the underworld, in a failed attempt to rescue his deceased wife, Izanami. Amaterasu was born when Izanagi washed his left eye, Tsukuyomi was born when he washed his right eye, and Susanoo was born when he washed his nose. Izanagi then appoints Amaterasu to rule Takamagahara (the "Plain of High Heaven"), Tsukuyomi the night, and Susanoo the seas.
 * The main narrative of the Nihon Shoki has Izanagi and Izanami procreating after creating the Japanese archipelago; to them were born (in the following order) Ōhirume-no-Muchi (Amaterasu), Tsukuyomi, the 'leech-child' Hiruko, and Susanoo:

"After this Izanagi no Mikoto and Izanami no Mikoto consulted together, saying:—'We have now produced the Great-eight-island country, with the mountains, rivers, herbs, and trees. Why should we not produce someone who shall be lord of the universe?' They then together produced the Sun-Goddess, who was called Oho-hiru-me no muchi. [...] The resplendent lustre of this child shone throughout all the six quarters. Therefore the two Deities rejoiced, saying:—'We have had many children, but none of them have been equal to this wondrous infant. She ought not to be kept long in this land, but we ought of our own accord to send her at once to Heaven, and entrust to her the affairs of Heaven.'

At this time Heaven and Earth were still not far separated, and therefore they sent her up to Heaven by the ladder of Heaven."

 * A variant legend recorded in the Shoki has Izanagi begetting Ōhirume (Amaterasu) by holding a bronze mirror in his left hand, Tsukuyomi by holding another mirror in his right hand, and Susanoo by turning his head and looking sideways.
 * A third variant in the Shoki has Izanagi and Izanami begetting the sun, the moon, Hiruko, and Susanoo, as in the main narrative. Their final child, the fire god Kagutsuchi, caused Izanami's death (as in the Kojiki).
 * A fourth variant relates a similar story to that found in the Kojiki, wherein the three gods are born when Izanagi washed himself in the river of Tachibana after going to Yomi.

Amaterasu and Tsukuyomi
One of the variant legends in the Shoki relates that Amaterasu ordered her brother Tsukuyomi to go down to the terrestrial world (Ashihara-no-Nakatsukuni, the "Central Land of Reed-Plains") and visit the goddess Ukemochi. When Ukemochi vomited foodstuffs out of her mouth and presented them to Tsukuyomi at a banquet, a disgusted and offended Tsukuyomi slew her and went back to Takamagahara. This act upset Amaterasu, causing her to split away from Tsukuyomi, thus separating night from day.

Amaterasu then sent another god, Ame-no-Kumahito (天熊人), who found various food-crops and animals emerging from Ukemochi's corpse.

"On the crown of her head there had been produced the ox and the horse; on the top of her forehead there had been produced millet; over her eyebrows there had been produced the silkworm; within her eyes there had been produced panic; in her belly there had been produced rice; in her genitals there had been produced wheat, large beans and small beans."

Amaterasu had the grains collected and sown for humanity's use and, putting the silkworms in her mouth, reeled thread from them. From this began agriculture and sericulture.

This account is not found in the Kojiki, where a similar story is instead told of Susanoo and the goddess Ōgetsuhime.

Amaterasu and Susanoo
When Susanoo, the youngest of the three divine siblings, was expelled by his father Izanagi for his troublesome nature and incessant wailing on account of missing his deceased mother Izanami, he first went up to Takamagahara to say farewell to Amaterasu. A suspicious Amaterasu went out to meet him dressed in male clothing and clad in armor, at which Susanoo proposed a trial by pledge (ukehi) to prove his sincerity. In the ritual, the two gods each chewed and spat out an object carried by the other (in some variants, an item they each possessed). Five (or six) gods and three goddesses were born as a result; Amaterasu adopted the males as her sons and gave the females – later known as the three Munakata goddesses – to Susanoo.

Susanoo, declaring that he had won the trial as he had produced deities of the required gender, then "raged with victory" and proceeded to wreak havoc by destroying his sister's rice fields and defecating in her palace. While Amaterasu tolerated Susanoo's behavior at first, his "misdeeds did not cease, but became even more flagrant" until one day, he bore a hole in the rooftop of Amaterasu's weaving hall and hurled the "heavenly piebald horse" (天斑駒, ame no fuchikoma), which he had flayed alive, into it. One of Amaterasu's weaving maidens was alarmed and struck her genitals against a weaving shuttle, killing her. In response, a furious Amaterasu shut herself inside the Ame-no-Iwayato (天岩屋戸, "Heavenly Rock-Cave Door", also known as Ama-no-Iwato), plunging heaven and earth into total darkness.

The main account in the Shoki has Amaterasu wounding herself with the shuttle when Susanoo threw the flayed horse in her weaving hall, while a variant account identifies the goddess who was killed during this incident as Wakahirume-no-Mikoto (稚日女尊, lit. "young woman of the sun / day(time)").

Whereas the above accounts identify Susanoo's flaying of the horse as the immediate cause for Amaterasu hiding herself, yet another variant in the Shoki instead portrays it to be Susanoo defecating in her seat: "In one writing it is said:—'The august Sun Goddess took an enclosed rice-field and made it her Imperial rice-field. Now Sosa no wo no Mikoto, in spring, filled up the channels and broke down the divisions, and in autumn, when the grain was formed, he forthwith stretched round them division ropes. Again when the Sun-Goddess was in her Weaving-Hall, he flayed alive a piebald colt and flung it into the Hall. In all these various matters his conduct was rude in the highest degree. Nevertheless, the Sun-Goddess, out of her friendship for him, was not indignant or resentful, but took everything calmly and with forbearance.

When the time came for the Sun-Goddess to celebrate the feast of first-fruits, Sosa no wo no Mikoto secretly voided excrement under her august seat in the New Palace. The Sun-Goddess, not knowing this, went straight there and took her seat. Accordingly the Sun-Goddess drew herself up, and was sickened. She therefore was enraged, and straightway took up her abode in the Rock-cave of Heaven, and fastened its Rock-door."

The Heavenly Rock Cave
After Amaterasu hid herself in the cave, the gods, led by Omoikane, the god of wisdom, conceived a plan to lure her out:

"[The gods] gathered together the long-crying birds of Tokoyo and caused them to cry. (...) They uprooted by the very roots the flourishing ma-sakaki trees of the mountain Ame-no-Kaguyama; to the upper branches they affixed long strings of myriad magatama beads; in the middle branches they hung a large-dimensioned mirror; in the lower branches they suspended white nikite cloth and blue nikite cloth.

These various objects were held in his hands by Futotama-no-Mikoto as solemn offerings, and Ame-no-Koyane-no-Mikoto intoned a solemn liturgy.

Ame-no-Tajikarao-no-Kami stood concealed beside the door, while Ame-no-Uzume-no-Mikoto bound up her sleeves with a cord of heavenly hikage vine, tied around her head a head-band of the heavenly masaki vine, bound together bundles of sasa leaves to hold in her hands, and overturning a bucket before the heavenly rock-cave door, stamped resoundingly upon it. Then she became divinely possessed, exposed her breasts, and pushed her skirt-band down to her genitals.

Then Takamanohara shook as the eight-hundred myriad deities laughed at once."

Inside the cave, Amaterasu is surprised that the gods should show such mirth in her absence. Ame-no-Uzume answered that they were celebrating because another god greater than her had appeared. Curious, Amaterasu slid the boulder blocking the cave's entrance and peeked out, at which Ame-no-Koyane and Futodama brought out the mirror (the Yata-no-Kagami) and held it before her. As Amaterasu, struck by her own reflection (apparently thinking it to be the other deity Ame-no-Uzume spoke of), approached the mirror, Ame-no-Tajikarao took her hand and pulled her out of the cave, which was then immediately sealed with a straw rope, preventing her from going back inside. Thus was light restored to the world.

As punishment for his unruly conduct, Susanoo was then driven out of Takamagahara by the other gods. Going down to earth, he arrived at the land of Izumo, where he killed the monstrous serpent Yamata no Orochi to rescue the goddess Kushinadahime, whom he eventually married. From the serpent's carcass Susanoo found the sword Ame-no-Murakumo-no-Tsurugi (天叢雲剣, "Sword of the Gathering Clouds of Heaven"), also known as Kusanagi-no-Tsurugi (草薙剣 "Grass-Cutting Sword"), which he presented to Amaterasu as a reconciliatory gift.

The subjugation of Ashihara-no-Nakatsukuni
After a time, Amaterasu and the primordial deity Takamimusubi (also known as Takagi-no-Kami) declared that Ashihara-no-Nakatsukuni, which was then being ruled over by Ōkuninushi (also known as Ō(a)namuchi), the descendant (Kojiki) or the son (Shoki) of Susanoo, should be pacified and put under the jurisdiction of their progeny, claiming it to be teeming with "numerous deities which shone with a lustre like that of fireflies, and evil deities which buzzed like flies". Amaterasu ordered Ame-no-Oshihomimi, the firstborn of the five male children born during her contest with Susanoo, to go down to earth and establish his rule over it. However, after inspecting the land below, he deemed it to be in an uproar and refused to go any further. At the advice of Omoikane and the other deities, Amaterasu then dispatched another of her five sons, Ame no Hohi. Upon arriving, however, Ame no Hohi began to curry favor with Ōkuninushi and did not send back any report for three years. The heavenly deities then sent a third messenger, Ame-no-Wakahiko, who also ended up siding with Ōkuninushi and marrying his daughter Shitateruhime. After eight years, a female pheasant was sent to question Ame-no-Wakahiko, who killed it with his bow and arrow. The blood-stained arrow flew straight up to Takamagahara at the feet of Amaterasu and Takamimusubi, who then threw it back to earth with a curse, killing Ame-no-Wakahiko in his sleep.

The preceding messengers having thus failed to complete their task, the heavenly gods finally sent the warrior deities Futsunushi and Takemikazuchi to remonstrate with Ōkuninushi. At the advice of his son Kotoshironushi, Ōkuninushi agreed to abdicate and left the physical realm to govern the unseen spirit world, which was given to him in exchange. The two gods then went around Ashihara-no-Nakatsukuni, killing those who resisted them and rewarding those who rendered submission, before going back to heaven.

With the earth now pacified, Amaterasu and Takamimusubi again commanded Ame-no-Oshihomimi to descend and rule it. He, however, again demurred and suggested that his son Ninigi be sent instead. Amaterasu thus bequeathed to Ninigi, the sword Susanoo gave her, along with the two items used to lure her out of the Ame-no-Iwayato: the mirror Yata-no-Kagami and the jewel Yasakani no Magatama. With a number of gods serving as his retinue, Ninigi came down from heaven to Mount Takachiho in the land of Himuka and built his palace there. Ninigi became the ancestor of the emperors of Japan, while the mirror, jewel, and sword he brought with him became the three sacred treasures of the imperial house. Five of the gods who accompanied him in his descent - Ame-no-Koyane, Futodama, Ame-no-Uzume, Ishikoridome (the maker of the mirror), and Tamanoya (the maker of the jewel) - meanwhile became the ancestors of the clans involved in court ceremonial such as the Nakatomi and the Inbe.

Emperor Jimmu and the Yatagarasu
Many years later, Ninigi's great-grandson, Kamuyamato-Iwarebiko (later known as Emperor Jimmu), decided to leave Himuka in search of a new home with his elder brother Itsuse. Migrating eastward, they encountered various gods and local tribes who either submitted to them or resisted them. After Itsuse died of wounds sustained during a battle against a chieftain named Nagasunehiko, Iwarebiko retreated and went to Kumano, located on the southern part of the Kii Peninsula. While there, he and his army were enchanted by a god in the shape of a giant bear and fell into a deep sleep. At that moment, a local named Takakuraji had a dream in which Amaterasu and Takamimusubi commanded the god Takemikazuchi to help Iwarebiko. Takemikazuchi then dropped his sword, Futsu-no-Mitama, into Takakuraji's storehouse, ordering him to give it to Iwarebiko. Upon waking up and discovering the sword inside the storehouse, Takakuraji went to where Iwarebiko was and presented it to him. The magic power of the Futsu-no-Mitama immediately exterminated the evil gods of the region and roused Iwarebiko and his men from their slumber.

Continuing their journey, the army soon found themselves stranded in the mountains. Takamimusubi (so the Kojiki) or Amaterasu (Shoki) then told Iwarebiko in a dream that the giant crow Yatagarasu would be sent to guide them in their way. Soon enough, the bird appeared and led Iwarebiko and his men to safety. At length, Iwarebiko arrived at the land of Yamato (modern Nara Prefecture) and defeated Nagasunehiko, thereby avenging his brother Itsuse. He then established his palace-capital at Kashihara and ruled therein.

Enshrinement in Ise
An anecdote concerning Emperor Sujin relates that Amaterasu (via the Yata-no-Kagami and the Kusanagi sword) and Yamato-no-Okunitama, the tutelary deity of Yamato, were originally worshipped in the great hall of the imperial palace. When a series of plagues broke out during Sujin's reign, he "dreaded [...] the power of these Gods, and did not feel secure in their dwelling together." He thus entrusted the mirror and the sword to his daughter Toyosukiiri-hime, who brought them to the village of Kasanuhi, and she would become the first Saiō. and delegated the worship of Yamato-no-Okunitama to another daughter, Nunakiirihime. When the pestilence showed no sign of abating, he then performed divination, which revealed the plague to have been caused by Ōmononushi, the god of Mount Miwa. When the god was offered proper worship as per his demands, the epidemic ceased.

During the reign of Sujin's son and successor, Emperor Suinin, custody of the sacred treasures were transferred from Toyosukiirihime to Suinin's daughter Yamatohime, who took them first to "Sasahata in Uda" to the east of Miwa. Heading north to Ōmi, she then eastwards to Mino and proceeded south to Ise, where she received a revelation from Amaterasu:

"Now Ama-terasu no Oho-kami instructed Yamato-hime no Mikoto, saying:—'The province of Ise, of the divine wind, is the land whither repair the waves from the eternal world, the successive waves. It is a secluded and pleasant land. In this land I wish to dwell.' In compliance, therefore, with the instruction of the Great Goddess, a shrine was erected to her in the province of Ise. Accordingly an Abstinence Palace was built at Kaha-kami in Isuzu. This was called the palace of Iso. It was there that Ama-terasu no Oho-kami first descended from Heaven."

This account serves as the origin myth of the Grand Shrine of Ise, Amaterasu's chief place of worship.

Later, when Suinin's grandson Prince Ousu (also known as Yamato Takeru) went to Ise to visit his aunt Yamatohime before going to conquer and pacify the eastern regions on the command of his father, Emperor Keikō, he was given the divine sword to protect him in times of peril. It eventually came in handy when Yamato Takeru was lured onto an open grassland by a treacherous chieftain, who then set fire to the grass to entrap him. Desperate, Yamato Takeru used the sword to cut the grass around him (a variant in the Shoki has the sword miraculously mow the grass of its own accord) and lit a counter-fire to keep the fire away. This incident explains the sword's name ("Grass Cutter"). On his way home from the east, Yamato Takeru – apparently blinded by hubris – left the Kusanagi in the care of his second wife, Miyazuhime of Owari, and went to confront the god of Mount Ibuki on his own. Without the sword's protection, he fell prey to the god's enchantment and became ill and died afterwards. Thus the Kusanagi stayed in Owari, where it was enshrined in the shrine of Atsuta.

Empress Jingū and Amaterasu's aramitama
At one time, when Emperor Chūai was on a campaign against the Kumaso tribes of Kyushu, his consort Jingū was possessed by unknown gods who told Chūai of a land rich in treasure located on the other side of the sea that is his for the taking. When Chūai doubted their words and accused them of being deceitful, the gods laid a curse upon him that he should die "without possessing this land." (The Kojiki and the Shoki diverge at this point: in the former, Chūai dies almost immediately after being cursed, while in the latter, he dies of a sudden illness a few months after.)

After Chūai's death, Jingū performed divination to ascertain which gods had spoken to her husband. The deities identified themselves as Tsukisakaki Izu no Mitama Amazakaru Mukatsuhime no Mikoto (撞賢木厳之御魂天疎向津媛命, "The Awe-inspiring Spirit of the Planted Sakaki, the Lady of Sky-distant Mukatsu", usually interpreted as the aramitama or 'violent spirit' of Amaterasu), Kotoshironushi, and the three gods of Sumie (Sumiyoshi): Uwatsutsunoo, Nakatsutsunoo, and Sokotsutsunoo. Worshiping the gods in accordance with their instructions, Jingū then set out to conquer the promised land beyond the sea: the three kingdoms of Korea.

When Jingū returned victorious to Japan, she enshrined the deities in places of their own choosing; Amaterasu, warning Jingū not to take her aramitama along to the capital, instructed her to install it in Hirota, the harbor where the empress disembarked.

Consorts
She is a virgin goddess and never engages in sexual relationships. However, according to Nozomu Kawamura, she was a consort to a sun god and some telling stories place Tsukuyomi as her husband.

Siblings
Amaterasu has many siblings most notably Susanoo and Tsukiyomi. Basil Hall Chamberlain used the words "elder brother" to translate her dialog referring to Susanoo in the Kojiki, even though he noted that she was his elder sister. The word (which was also used by Izanami to address her elder brother and husband Izanagi) was nase (phonetically spelt 那勢 in the Kojiki; modern dictionaries use the semantic spelling 汝兄, whose kanji literally mean "my elder brother"), an ancient term used only by females to refer to their brothers, who had higher status than them. (As opposed to males using nanimo (汝妹) (那邇妹 in the Kojiki) to refer to their sisters, who had lower status than them.) The Nihon Shoki used the Chinese word 弟 ("younger brother") instead.

Some tellings say she had a sister named Wakahirume who was a weaving maiden and helped Amaterasu weave clothes for the other kami in heaven. Wakahirume was later accidentally killed by Susanoo.

Other traditions say she had an older brother named Hiruko.

Descendants
Amaterasu has 5 sons Ame-no-oshihomimi, Ame no Hohi, Amatsuhikone, Ikutsuhikone, and Kumanokusubi, who were given birth to by Susanoo by chewing her hair jewels. According to one account in the Nihon Shoki, it was because these children were male that Susanoo won during the ritual to prove his intent, even though they were not his children, but hers. This explanation of the outcome of the ritual contradicts that in the Kojiki, according to which it was because she gave birth to female children using his sword, and those children were his. The Kojiki claims he won because he had daughters to whom she gave birth, while the Nihon Shoki claims he won because he himself gave birth to her sons. Several figures and noble clans claim descent from Amaterasu most notably the Japanese imperial family through Emperor Jimmu who descended from her grandson Ninigi.

Her son Ame no Hohi is considered the ancestral kami of clans in Izumo which includes the Haji clan, Sugawara clan, and the Senge clan. The legendary sumo wrestler Nomi no Sukune is believed to be a 14th generation descendant of Amenohohi.

Worship

The Ise Grand Shrine (伊勢神宮 Ise Jingū) located in Ise, Mie Prefecture, Japan, houses the inner shrine, Naiku, dedicated to Amaterasu. Her sacred mirror, Yata no Kagami, is said to be kept at this shrine as one of the Imperial regalia objects. A ceremony known as Jingū Shikinen Sengū (神宮式年遷宮) is held every twenty years at this shrine to honor the many deities enshrined, which is formed by 125 shrines altogether. New shrine buildings are built at a location adjacent to the site first. After the transfer of the object of worship, new clothing and treasure and offering food to the goddess the old buildings are taken apart. The building materials taken apart are given to many other shrines and buildings to renovate. This practice is a part of the Shinto faith and has been practiced since the year 690 CE, but is not only for Amaterasu but also for many other deities enshrined in Ise Grand Shrine. Additionally, from the late 7th century to the 14th century, an unmarried princess of the Imperial Family, called "Saiō" (斎王) or itsuki no miko (斎皇女), served as the sacred priestess of Amaterasu at the Ise Shrine upon every new dynasty.

The Amanoiwato Shrine (天岩戸神社) in Takachiho, Miyazaki Prefecture, Japan is also dedicated to Amaterasu and sits above the gorge containing Ama-no-Iwato.

The worship of Amaterasu to the exclusion of other kami has been described as "the cult of the sun." This phrase may also refer to the early pre-archipelagoan worship of the sun.

According to the Engishiki (延喜式) and Sandai Jitsuroku (三代実録) of the Heian period, the sun goddess had many shrines named "Amateru" or "Amateru-mitama", which were mostly located in the Kinki area. However, there have also been records of a shrine on Tsushima Island, coined as either "Teruhi Gongen" or the "Shining Sun Deity" during medieval times. It was later found that such a shrine was meant for a male sun deity named Ameno-himitama.

Amaterasu was also once worshiped at Hinokuma shrines. The Hinokuma shrines were used to worship the goddess by the Ama people in the Kii Provinces. Because the Ama people were believed to have been fishermen, researchers have conjectured that the goddess was also worshiped for a possible connection to the sea.

Amaterasu was thought by some in the early 20th century until after World War II to have "created the Japanese archipelago from the drops of water that fell from her spear" and in historic times, the spear was an item compared to the sun and solar deities.

Differences in worship
Amaterasu, while primarily being the goddess of the sun, is also sometimes worshiped as having connections with other aspects and forms of nature. Amaterasu can also be considered a goddess of the wind and typhoons alongside her brother, and even possibly death. There are many connections between local legends in the Ise region with other goddesses of nature, such as a nameless goddess of the underworld and sea. It's possible that Amaterasu's name became associated with these legends in the Shinto religion as it grew throughout Japan.

One source interprets from the Heavenly Rock Cave myth that Amaterasu was seen as being responsible for the normal cycle of day and night.

A historical myth holds that she painted the islands of Japan into being, alongside her siblings Susanoo and Tsukuyomi.

In contrast, Amaterasu, while enshrined at other locations, also can be seen as the goddess that represents Japan and its ethnicity. The many differences in Shinto religion and mythology can be due to how different local gods and beliefs clashed. In the Meiji Era, the belief in Amaterasu fought against the Izumo belief in Ōkuninushi for spiritual control over the land of Japan. During this time, the religious nature of Okininushi may have been changed to be included in Shinto mythology. Osagawara Shouzo built shrines in other countries to mainly spread Japan's culture and Shinto religion. It, however, was usually seen as the worshiping of Japan itself, rather than Amaterasu. Most of these colonial and oversea shrines were destroyed after WWII.

Snake
Outside of being worshiped as a sun goddess, some have argued that Amaterasu was once related to snakes. There was a legend circulating among the Ise Priests that essentially described an encounter of Amaterasu sleeping with the Saiō every night in the form of a snake or lizard, evidenced by fallen scales in the priestess' bed. This was recorded by a medieval monk in his diary, which stated that "in ancient times Amaterasu was regarded as a snake deity or as a sun deity." In the Ise kanjō, the god's snake form is considered an embodiment of the "three poisons", namely greed, anger, and ignorance. Amaterasu is also linked to a snake cult, which is also tied to the theory that the initial gender of the goddess was male.

Dragon
In general, some of these Amaterasu–dragon associations have been in reference to Japanese plays. One example has been within the Chikubushima tradition in which the dragon goddess Benzaiten was the emanation of Amaterasu. Following that, in the Japanese epic, Taiheki, one of the characters, Nitta Yoshisada (新田義貞), made comparisons with Amaterasu and a dragon with the quote: “I have heard that the Sun Goddess of Ise … conceals her true being in the august image of Vairocana, and that she has appeared in this world in the guise of a dragon god of the blue ocean.”

Another tradition of the Heavenly Cave story depicts Amaterasu as a "dragon-fox" (shinko or tatsugitsune) during her descent to the famed cave because it is a type of animal/kami that emits light from its entire body.

Relation to women's positions in early Japanese society
Because Amaterasu has the highest position among the Shinto deities, there has been debate on her influence and relation to women's positions in early Japanese society. Some scholars have argued that the goddess' presence and high stature within the kami system could suggest that early rulers in Japan were female. Others have argued the goddess' presence implies strong influences female priests had in Japanese politics and religion.

title: Amaterasu


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Thermodynamic free energy

In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system (the others being internal energy, enthalpy, entropy, etc.). The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy. Several free energy functions may be formulated based on system criteria. Free energy functions are Legendre transforms of the internal energy.

The Gibbs free energy is given by $G = H − TS$, where $H$ is the enthalpy, $T$ is the absolute temperature, and $S$ is the entropy. $H = U + pV$, where $U$ is the internal energy, $p$ is the pressure, and $V$ is the volume. $G$ is the most useful for processes involving a system at constant pressure $p$ and temperature $T$, because, in addition to subsuming any entropy change due merely to heat, a change in $G$ also excludes the $p dV$ work needed to "make space for additional molecules" produced by various processes. Gibbs free energy change therefore equals work not associated with system expansion or compression, at constant temperature and pressure, hence its utility to solution-phase chemists, including biochemists.

The historically earlier Helmholtz free energy is defined in contrast as $A = U − TS$. Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant $T$. Thus its appellation "work content", and the designation $A$. Since it makes no reference to any quantities involved in work (such as $p$ and $V$), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by a system at constant temperature, and it can increase at most by the amount of work done on a system isothermally. The Helmholtz free energy has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore $p dV$ work.)

Historically, the term 'free energy' has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy, denoted by $A$ (or $F$), while in chemistry, free energy most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations.

Meaning of "free"
The basic definition of "energy" is a measure of a body's (in thermodynamics, the system's) ability to cause change. For example, when a person pushes a heavy box a few metres forward, that person exerts mechanical energy, also known as work, on the box over a distance of a few meters forward. The mathematical definition of this form of energy is the product of the force exerted on the object and the distance by which the box moved (Work = Force × Distance). Because the person changed the stationary position of the box, that person exerted energy on that box. The work exerted can also be called "useful energy", because energy was converted from one form into the intended purpose, i.e. mechanical use. For the case of the person pushing the box, the energy in the form of internal (or potential) energy obtained through metabolism was converted into work to push the box. This energy conversion, however, was not straightforward: while some internal energy went into pushing the box, some was diverted away (lost) in the form of heat (transferred thermal energy).

For a reversible process, heat is the product of the absolute temperature $$T$$ and the change in entropy $$S$$ of a body (entropy is a measure of disorder in a system). The difference between the change in internal energy, which is $$\Delta U$$, and the energy lost in the form of heat is what is called the "useful energy" of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as "free energy". In other words, free energy is a measure of work (useful energy) a system can perform at constant temperature.

Mathematically, free energy is expressed as

$$A=U-TS$$

This expression has commonly been interpreted to mean that work is extracted from the internal energy $$U$$ while $$TS$$ represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the internal energy change is $$\Delta U=0$$ and the expansion work $$w=-T\Delta S$$ is derived exclusively from the $$TS$$ term supposedly not available to perform work. But it is noteworthy that the derivative form of the free energy: $$dA=-SdT-PdV$$ (for Helmholtz free energy) does indeed indicate that a spontaneous change in a non-reactive system's free energy (NOT the internal energy) comprises the available energy to do work (compression in this case) $$-PdV$$ and the unavailable energy $$-SdT$$. Similar expression can be written for the Gibbs free energy change.

In the 18th and 19th centuries, the theory of heat, i.e., that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the caloric theory, i.e., that heat is a fluid, and the four element theory, in which heat was the lightest of the four elements. In a similar manner, during these years, heat was beginning to be distinguished into different classification categories, such as "free heat", "combined heat", "radiant heat", specific heat, heat capacity, "absolute heat", "latent caloric", "free" or "perceptible" caloric (calorique sensible), among others.

In 1780, for example, Laplace and Lavoisier stated: “In general, one can change the first hypothesis into the second by changing the words ‘free heat, combined heat, and heat released’ into ‘vis viva, loss of vis viva, and increase of vis viva.’" In this manner, the total mass of caloric in a body, called absolute heat, was regarded as a mixture of two components; the free or perceptible caloric could affect a thermometer, whereas the other component, the latent caloric, could not. The use of the words "latent heat" implied a similarity to latent heat in the more usual sense; it was regarded as chemically bound to the molecules of the body.  In the adiabatic compression of a gas, the absolute heat remained constant but the observed rise in temperature implied that some latent caloric had become "free" or perceptible.

During the early 19th century, the concept of perceptible or free caloric began to be referred to as "free heat" or "heat set free". In 1824, for example, the French physicist Sadi Carnot, in his famous "Reflections on the Motive Power of Fire", speaks of quantities of heat ‘absorbed or set free’ in different transformations. In 1882, the German physicist and physiologist Hermann von Helmholtz coined the phrase ‘free energy’ for the expression $$A=U-TS$$, in which the change in A (or G) determines the amount of energy ‘free’ for work under the given conditions, specifically constant temperature.

Thus, in traditional use, the term "free" was attached to Gibbs free energy for systems at constant pressure and temperature, or to Helmholtz free energy for systems at constant temperature, to mean ‘available in the form of useful work.’ With reference to the Gibbs free energy, we need to add the qualification that it is the energy free for non-volume work and compositional changes.

An increasing number of books and journal articles do not include the attachment "free", referring to G as simply Gibbs energy (and likewise for the Helmholtz energy). This is the result of a 1988 IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished. This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’.

Application
Just like the general concept of energy, free energy has a few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature $$T$$, volume $$V$$, pressure $$p$$, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is:

 * $$A = U-TS$$

This definition of free energy is useful for gas-phase reactions or in physics when modeling the behavior of isolated systems kept at a constant volume. For example, if a researcher wanted to perform a combustion reaction in a bomb calorimeter, the volume is kept constant throughout the course of a reaction. Therefore, the heat of the reaction is a direct measure of the free energy change, $$q=\Delta U$$. In solution chemistry, on the other hand, most chemical reactions are kept at constant pressure. Under this condition, the heat $$q$$ of the reaction is equal to the enthalpy change $$\Delta H$$ of the system. Under constant pressure and temperature, the free energy in a reaction is known as Gibbs free energy $$G$$.

 * $$G = H-TS$$

These functions have a minimum in chemical equilibrium, as long as certain variables ($$T$$, and $$V$$ or $$p$$) are held constant. In addition, they also have theoretical importance in deriving Maxwell relations. Work other than p dV may be added, e.g., for electrochemical cells, or f dx work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors.

In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.

$$N_i$$ is the number of molecules (alternatively, moles) of type $$i$$ in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differentials for processes at uniform pressure and temperature are (assuming only $$pV$$ work):

 * $$\mathrm dA = - p\,\mathrm dV - S\,\mathrm dT + \sum_i \mu_i \,\mathrm dN_i\,$$

 * $$\mathrm dG = V\,\mathrm dp - S\,\mathrm dT + \sum_i \mu_i \,\mathrm dN_i\,$$

where μi is the chemical potential for the ith component in the system. The second relation is especially useful at constant $$T$$ and $$p$$, conditions which are easy to achieve experimentally, and which approximately characterize living creatures. Under these conditions, it simplifies to

 * $$(\mathrm dG)_{T,p} = \sum_i \mu_i \,\mathrm dN_i\,$$

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as $$T$$ times a corresponding increase in the entropy of the system and/or its surrounding.

An example is surface free energy, the amount of increase of free energy when the area of surface increases by every unit area.

The path integral Monte Carlo method is a numerical approach for determining the values of free energies, based on quantum dynamical principles.

Work and free energy change
For a reversible isothermal process, ΔS = qrev/T and therefore the definition of A results in

 * $$\Delta A = \Delta U - T \Delta S = \Delta U - q_\text{rev} = w_\text{rev}$$ (at constant temperature)

This tells us that the change in free energy equals the reversible or maximum work for a process performed at constant temperature. Under other conditions, free-energy change is not equal to work; for instance, for a reversible adiabatic expansion of an ideal gas, $\Delta A = w_\text{rev} - S \Delta T$. Importantly, for a heat engine, including the Carnot cycle, the free-energy change after a full cycle is zero, $\Delta_\text{cyc} A = 0 $, while the engine produces nonzero work. It is important to note that for heat engines and other thermal systems, the free energies do not offer convenient characterizations; internal energy and enthalpy are the preferred potentials for characterizing thermal systems.

Free energy change and spontaneous processes
According to the second law of thermodynamics, for any process that occurs in a closed system, the inequality of Clausius, ΔS > q/Tsurr, applies. For a process at constant temperature and pressure without non-PV work, this inequality transforms into $$\Delta G < 0 $$. Similarly, for a process at constant temperature and volume, $$\Delta A < 0 $$. Thus, a negative value of the change in free energy is a necessary condition for a process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0.

History
The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, which was used by chemists in previous years to describe the force that caused chemical reactions. The term affinity, as used in chemical relation, dates back to at least the time of Albertus Magnus.

From the 1998 textbook Modern Thermodynamics by Nobel Laureate and chemistry professor Ilya Prigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points?  Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition."

During the entire 18th century, the dominant view with regard to heat and light was that put forth by Isaac Newton, called the Newtonian hypothesis, which states that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity.

In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat.

In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the specific heat and latent heat of a number of substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step process or in a number of stages. This is known as Hess' law. With the advent of the mechanical theory of heat in the early 19th century, Hess's law came to be viewed as a consequence of the law of conservation of energy.

Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the English physicist James Joule showed that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i.e., approximately, dW ∝ dQ. This statement came to be known as the mechanical equivalent of heat and was a precursory form of the first law of thermodynamics.

By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment. That is, one can use the heat derived from a combustion reaction in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push a piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i.e., the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e.g., from ($$P_1,V_1$$) to ($$P_2,V_2$$). Clausius originally called this the "transformation content" of the body, and then later changed the name to entropy. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e.g., to push the piston. Clausius defined this transformation heat as $$dQ=TdS$$.

In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other. In his own words, to summarize his results in 1873, Gibbs states:

"If we wish to express in a single equation the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded by a medium of constant pressure p and temperature T, this equation may be written:

when δ refers to the variation produced by any variations in the state of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum."

In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy of the body, and ν is the volume of the body.

Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas' hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy A at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (Internal energy). Thus, G or A is the amount of energy "free" for work under the given conditions.

Up until this point, the general view had been such that: “all chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanish”. Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian Henry Leicester, the influential 1923 textbook Thermodynamics and the Free Energy of Chemical Reactions by Gilbert N. Lewis and Merle Randall led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.

title: Thermodynamic free energy