text:
Talk:H-theorem

Origin of the H formula ?
how did boltzmann come up with his definition for H? (Yosofun 06:42, 12 Apr 2005 (UTC))

Fluctuation theorem
I'm cutting the following line:

 * The final resolution of the time reversibility paradox is found in the Fluctuation Theorem.

There is stuff which could be said about the Fluctuation Theorem as a modern generalisation of work on the prediction of entropy increase.

But the FT has nothing to say about the Arrow of time, because, like Boltzmann's H-theorem, the entropy increase it predicts so well arises because one assumes one can ignore correlations and similar 'hidden information' at times after the initial time. If you start with a non-equilibrium state and try to use the Fluctuation Theorem to predict backwards how that non-equilibrium state came to be, it will predict that it arose spontaneously as a fluctuation from an equilibium state -- because those are the only possibilities it knows about.

The cause of time asymmetry in the observed universe must be looked for elsewhere. Jheald 12:28, 21 October 2005 (UTC)

Hi everybody!
While reading my personal copy of Tolman's book and I saw the chapter on H - theorem The Shannon information entropy, which is talked about in another book I have been reading by Feynman called lectures on computation contains a lot about Shannon's ideas. I find this subject interesting and I can help with the article with some inline citations if I can find something that Toleman said in his book inside of the article that needs an inline source

According to the history of entropy article Shannon information entropy is related to "H" and interestingly Shannon recognized his same formula by reading the same book I am reading now Toleman.

By the way Jheald, nice to see you have been working on this article! Also thanks so much for recommending the Penrose book, I have been studying it very intently. I am kinda stuck on chapter 12 but I have been skipping ahead and reading the later chapters as well.

Penrose seems to talk about just about everything in his book, but don't remember H theorem, and yes I have looked in the index but was wondering if it was called something else.

Hobojaks (talk) 07:00, 22 February 2009 (UTC)

 * Note that Tolman was written in 1938, though it's still an outstanding book. Shannon only widely introduced the idea of the Shannon entropy ten years later.  Relationships between the two are touched on here in the Shannon entropy article.  They are still the subject of some controversy.  The link between the two ideas has been propounded most vigorously by E.T. Jaynes and his subsequent followers, from 1957 onwards; others still decry it, though as early as 1930 G.N. Lewis had written that "Gain in entropy always means loss of information, and nothing more".

 * Penrose touches on the idea of the H-theorem, and the related issue of Loschmidt's paradox in section 27.5 (page 696 in the UK hardback); though he doesn't mention either by name, essentially takes the idea of coarse graining as read, and quickly moves on to the gravitational and cosmological issues he's most interested in.

 * H.D. Zeh's The Physical Basis of the Direction of Time, now into its fifth edition, is often given as the standard overview reference in this area; though note that it's written at a professional level, not a popular one. Chapter 3 looks at thermodynamics, before the book gets into decoherence and then black hole and cosmological thermodynamics.  Jheald (talk) 11:03, 22 February 2009 (UTC)

Been reading Tolman
But I have to say it is a pretty hard book to digest in a short while. I get the feeling that I am going to be reading it for quite some time, because I find the section on quantum mechanics particularly difficult, and yet required to understand some of his most profound ideas.

I found an article on Boltzmann_entropy which I am starting to understand is related to H.

The citations I found from Tolman so far, don't need to go in the first paragraph if this makes the first paragraph seem to wordy, but I think the actual page numbers and wording might actually belong someplace at least in the article?

One thing that I have found in my experience to be true is that citations take more work than typing, so maybe the main contribution here is providing actual inline page numbers to a source for some of the material.

 * Um, I don't want to sound overbearing, and it's really good the way you're working through this; but can I suggest that you wait until you understand what is in the article first, so that you're confident you have a solid grasp of the big picture first, before you start trying to rewrite it?

 * While you're getting there, questions like "I don't understand this" or "This doesn't seem quite right to me" or "Why is the article saying that" are maybe more useful than trying to rewrite it as you're going along.

 * If you have access to a good university library, you also might find that some more modern "introduction to statistical mechanics" books may give a quicker, more accessible presentation. It's always good to have a look at what more than one source of exposition is saying (and the references would be good for the article, too!)  Jheald (talk) 21:35, 24 February 2009 (UTC)

 * I'm not saying there isn't a lot wrong with this article, because there most definitely is. But I do think the best way to fix it is from the big picture first; i.e. to do some fairly comprehensive reading first, and work out what the most important things we want to say are first, rather than starting in on it piecemeal.  Jheald (talk) 22:30, 24 February 2009 (UTC)

 * I agree to this methodology. However this suggests a more major undertaking than I had originally planned.  I had at first thought to work on providing inline citations to the existing article with possibly some slight rewordings to bring the wikipedia text into agreement with those sources.  That is OK though because the more I learn about H theorem the more interesting it becomes.  Also the concept of the H theorem is deeper and more complicated than I first thought it would be!  I especially appreciate your help in working through this. I am sure that there are both passive current and future readers of this discussion who are, or will be equally grateful for your contributions.

Hobojaks (talk) 21:08, 25 February 2009 (UTC)

Some material for possible inclusion
In classical thermodynamics, the H-theorem was a thermodynamic principle first introduced by Boltzmann in 1872. The H-theorem demonstrates the tendency of the molecules of a system to approach their equilibrium Maxwell-Boltzmann distribution. The quantity called H by Boltzmann can be regraded as an appropriate measure of the extent to which the condition of the system deviates from that corresponding to equilibrium. This quantity H has a tendency to decrease with time to a minimum and thus for the system to approach its equilibrium condition. .

The H-theorem has been restated in quantum mechanical form.

The decrease in the quantity H is related to the increase in the entropy

. For example the approach to equilibrium of an ideal gas in an irreversible process, can be demonstrated using an approach based on the Boltzmann equation.

It appears to predict an irreversible increase in entropy, despite microscopically reversible dynamics. This has led to much discussion.

ergodic hypothesis —Preceding unsigned comment added by 76.191.171.210 (talk) 07:23, 24 February 2009 (UTC)

Hobojaks (talk) 19:41, 23 February 2009 (UTC)

Problem list
The quantity H is defined as the integral over velocity space :
 * {| style="width:100%" border="0"

$$  \displaystyle H   \ \stackrel{\mathrm{def}}{=}\ \int { P ({\ln P}) d^3 v}   = \left\langle { \ln P } \right\rangle $$ where P(v) is the probability. H is a forerunner of Shannon's information entropy.
 * style="width:95%" |
 * style="width:95%" |
 * style= | (1)
 * }

(1) Exactly what is velocity space would it be better to call it phase space

 * The integral isn't over phase space. That was an adaptation suggested by Gibbs some years later.  (Tolman p. 165 and onwards).  Boltzmann's original integral was over the 3-dimensional space of possible molecular velocities, not the 6N-dimensional phase space.

 * Actually I have managed to find somewhat of a source for this. But it is only in a problem set.  The source is Fundamentals of statistical and thermal physics, Rieff 1965,  The index lists two places were it talks about H theorem the first is in a problem set.  These problems do define H as an integral containing a $$d^3$$ term.  But it is multiplied by a distribution function, times the log of a distribution function, which is just a little different from a probability.  So still no source for the current formula, but possibly just the slightest hope for it?Hobojaks (talk) 04:05, 27 February 2009 (UTC)

 * On further consideration, it looks like this may well be wrong. Tolman presents Boltzmann as working in a 6-dimensional "μ-space".  (Not the 6N-dimensional phase space, though).

 * On the other hand, the key input to the H-theorem is the time-reversibility of the transition coefficients. I don't think that depends on position, so it may not be impossible that Boltzmann first presented the derivation purely for the velocity distribution.  We would need to check a reference that actually goes into the detail of the development of Boltzmann's thought to be sure - probably something by S. Brush. Jheald (talk) 22:12, 24 February 2009 (UTC)

 * I have been studying Toleman pg 45 as near as I can tell, "μ-space" is one of two flavors of phase space which he draws a distinction between. "...The phase space for any individual kind of element (molecule) is called the μ-space for that species of element."  The other flavor of phase space is gama-space.  According to Toleman the key distinction of "μ-space" is that if you switch two identical molecules this does not really count as two different states in "μ-space", but it would gama-space. Hobojaks (talk) 23:20, 25 February 2009 (UTC)  I have discovered that in addition to page 45 the whole section 27 starting on page 74 is dedicated to explaining "μ-space".  In section 27 it is made clear that "μ-space" is the phase space of a single molecule, and that a gamma-space for the whole system of many identical molecules can be made up by combining all the μ-spaces of the individual particles.  He then explains a procedure for eliminating all the permutations that come about by switching two identical particles, adding that this concept will be of great importance when switching to quantum mechanics. μ-space in the case of a single molecule of a mono atomic gas would be six dimensional but in general the μ-space of a molecule would have 2f dimensions corresponding the the each of the generalized coordinates and generalized momentum for each degree of freedom p & q Hobojaks (talk) 08:43, 26 February 2009 (UTC)

1(a) Also a problem with the formula in question is that it says that P is the probability but it does not say the probability of what. I have found a citation in Rief Fundamentals of Statistical and thermal physics which may be relevant. This formula is for a limited special case of an ideal mono-atomic gas, and the problem tells the student to assume that for f they can use the equilibrium Maxwell distribution.

$$H=\int d^3\mathbf{v} f\,\log\,f$$

The student is then ask to show that H = -S/k where S is the entropy per unit volume of a mono-atomic ideal gas.

Is perhaps the student being guided down the path that Boltzmann once followed. I can't be sure of this, but I can make one observation. There needs to be a symbol for two different versions of H. One for the extensive property of the entire system and one for the intensive property. The H in the specialized Rieff-Boltzmann H theorem is the H per unit volume, and clearly not the H for the 'system' as a whole. This is a point that I struggled with considerably, and would like to get conformation that I am correct on?

In order to prevent future readers of this article from suffering the difficulty I have suffered I propose that we develop some notation to distinguish between H and H per unit volume in the article, and clearly indicate which one we are talking about each time we indicate a formula!!!!

Note that Toleman's formulas for H also use the notation were there is an f function, but where f is more generalized.

Perhaps a substitution were f is substituted for P and it is clearly stated that f is the equilibrium Maxwell distribution, and that the formula is specialized is in order. Note that the start of the article gives a very restricted definition for the H theorem, which is no longer true of the more general presentation the article currently gives.

(2) I can't find this exact formula for H anywhere in Tolman, who lists a number of different forms. It looks like there is a strange cube term on the differential operator, like it is the third derivative of v, which I guess is velocity space, the article really does not say.

 * It's maybe an evolution of notation since Tolman's time, but the meaning is quite clear. The d3 v is being used as a shorthand for dv1 dv2 dv3.

(3) Shouldn't there be multiple integration symbols. $$\int... \int$$

 * Again, it's an evolution of notation. The integral is understood to be an integral over volume elements d3 v, rather than considering it a series of line integrals.  The use of a single integral sign to indicate an integral over all the elements of a set is not unusual.

(4) Would it be better to have $$\delta p\,$$ and $$\delta q\,$$ indicating an inexact differentials of momentum and generalized coordinate? Especially in a variant of the formula that uses a summation rather than an integration?

 * Boltzmann's integral wasn't an integral over phase space, it was an integral over velocity space.

(5) As near as I can tell there are at least three different versions of H theorem, at least in the context that Tolman uses the term. There is the original version of Boltzmann then there is the version of Gibbs which modifies Boltzmann's early version. Then there is the quantum mechanical version.

 * Yes. This is something the article could perhaps make clearer.  The basic structure of the argument is the same in each case however.  The quantum mechanical version is (IMO) the one that is most stripped down to fundamentals, and easiest to see what is going on, so in my view it is the right choice that that is the one the article chooses to show how the H theorem comes about.

(6)There is another redefinition of entropy currently underway, that includes the concept that a black hole can have an entropy. Yet this new black hole including version of entropy is in contradiction with H theorem, at least if I understand correctly, but this is neglected in the article.

 * See Black hole information paradox, and in particular recent discussions on the talk page there. There is sort of a connection - in both cases information you used to have about the system is being thrown away in your later description of the system, despite a deterministic evolution.  With the H-theorem we know how that's happening.  With the BH information paradox it is yet quite not so clear.  It may be because the BH is not always being described in a fully quantum mechanical way, with a definitely finite number of states; it may also be related to information becoming unobservable in decoherence.

 * Zeh has written on this and it is covered in his book; but I don't think raising the issue of BH unitarity, which is still quite murky, is helpful in understanding the H-theorem, which is much simpler, and is well understood. It might be worth a mention in the "See also" section, if one could judiciously word the right covering phrase to make the connection. But anything else here would be a unnecessary diversion into confusion, when what we should be trying to do is make the main ideas and issues with the H theorem come over as clearly and simply as we can.

(7)Some older authors (including Tolman) equate H with the macroscopic entropy, it seems this important idea has taken a back seat to the idea of equating H to Shannon entropy? According to Tolman this association is one of the greatest achievements of physics.

 * No, I think what Tolman is saying is quite right. The connection with Shannon entropy (for those who accept the connection) just makes the achievement even richer.

 * Gibbs's version of H (and its quantum analogue) - apart from a minus sign, and a completely irrelevant factor of kB - is essentially the standard, most general expression for microscopic entropy. I would say that the identification of this entropy at a microscopic level with classical thermodynamic entropy, so that one can write
 * $$S = -k \sum p \log p$$
 * is definitely one of the greatest achievements of physics, without any doubt whatsoever.

 * If you go with Jaynes then Shannon's work makes Gibbs's formula even more of a fundamental intellectual achievement, because Shannon's work tells us that we can give a precise meaning to what is quite an abstract mathematics. Shannon shows that Gibbs's - Σ p ln p is the natural measure of information.  So the H in the formula precisely connects information with classical thermodynamic entropy.  The importance of H is precisely that it connects with both.

 * But classical thermodynamic entropy increases. How can we relate that to an amount of information, and to deterministic dynamics?  This is where the H theorem comes in.  It shows that if we approximate what's going on in the molecular collisions, or in quantum processes, making the processes probabilistic instead of deterministic because we can't keep track of the full details of the system - i.e. if the only information we can keep track of is in the macroscopic variables, then we systematically lose information; so if we use S to describe classical thermodynamic entropy, which is a state function of the macroscopic variables of the system, S will tend to increase.

 * So in short: the idea, that S given by the formula above, directly relates to classical thermodynamic entropy, is and remains absolutely fundamental.

 * The further idea, that that S can naturally be interpreted as the amount of Shannon information, which would be needed to define the microscopic system fully, but which is not conveyed by macroscopic variables alone, is the icing on the cake, which people can take or leave according to taste. Jheald (talk) 21:16, 24 February 2009 (UTC)
 * I think a lot of the hostility shown towards Shannon's information entropy is a gut feeling that it somehow dilutes Boltzmann's (and Gibbs's) great achievement! It doesn't, of course, as Shannon's contribution is only secondary and derivative :P Physchim62 (talk) 23:59, 25 February 2009 (UTC)

8 There are actually two classical forms of H theorem. The original old school Boltzmann version and the 1902 Gibbs version, based on a different quantity which is essentially the value of double bar H in Toleman's notation. This latter idea is a quantity "which characterizes the condition of the ensemble of systems which we use as appropriate for representing the continued behavior of the actual system of interest."(Toleman pg 166)

Some important formula
It would seem to me that equations 47.5 to 47.9 of on page 135 - 136 of tolemans book in the section titled definition of the quantity H are very important. When I get chance I will start to transcribe these here for possible inclusion. —Preceding unsigned comment added by Hobojaks (talk • contribs) 21:14, 24 February 2009 (UTC)

 * They are all variants on $$H = \sum p_i \log p_i$$, which is really the key idea. Best to go with that, I think.  Jheald (talk) 22:36, 24 February 2009 (UTC)

A good inline reference for that formula would be (Toleman 1938 pg 460 formula 104.7)

If you look closely in that version there is a double bar over the H, and it might be nice to have the double bar over the wikipedia version as well. Apparently in Toleman's thinking double bar H is a property of an ensemble where as H with no bar is a property of an individual system.

Hobojaks (talk) 20:46, 25 February 2009 (UTC)
 * Something like H  or $$\overline{\overline{H}}$$? Physchim62 (talk) 12:29, 26 February 2009 (UTC)

$$\overline{\overline{H}}= \sum p_k \log p_k$$

This now looks exactly like the text from toleman's chapter The Quantum Mechanical H-theorem. Maybe someone can help me that understands the guidelines for inline citations to get the formant exactly correct for this important citation but then I propose that we include this line in the article.

It may also be wise to start with the 'quantum mechanical' formula as J heald has suggested using the rational that it is the simplest form of H theorem.

 * Not just that, but it gives a nice general notation based on transition probabilities between states, into which terms the classical versions can easily be cast as well. Jheald (talk) 11:26, 1 March 2009 (UTC)

The double bar tells us that we must constantly remember that this is not a property of a single system but an average property of an ensemble of systems.

 * I would use H, without the double bar, for the first time you are introducing the system. -- After all, it's only Tolman who uses the double bar, it's not "standard" notation.  For other uses, we could than qualify H in difference ways, eg perhaps with a subscript, if we really want to emphasise that it is being calculated for a different probability distribution.  Jheald (talk) 11:26, 1 March 2009 (UTC)

Also since we are contemplating including in this article boltzmann's original H quantity it will help to distinguish between the two quantities.

As a side note, Gibbs has a really nasty habit of stealing other peoples terminology, and introducing his own ideas, under the same name as another concept. Boltzmann's H-theorem, Clausisus's entropy, and Hamilton's vector are important on this list.

I have not really found anybody who has commented on the somewhat cosmic significance of the fact that in fact Boltzmann proved that the "true entropy" has to be a negative quantity. Sign switching was something that Gibbs delighted in, also switching the sign of the scalar part of the square of a quaternion. Hence V 'dot' V = $$-V^2$$ with Gibb's hermaphrodidical notation on the right, and Hamilton's in my point of view more elegant notation on the right. It would be interesting of a citation for this observation could be found, because I don't think it is OR on my part? It is in part what drives my interest in H - theorem. My other favorite book on thermodynamics relegates H -theorem to an apendex. Yet still a good source.Hobojaks (talk) 19:15, 26 February 2009 (UTC)

Plan for a little editing.
1)Complete, I am changing the order of the quantum mechanical version of H theorem, with the other section.

As per discussion this is the more relevant definition of H theorem. This may require some cleanup.

(2)Complete, I am moving the discussion of Shannon entropy into the first quantum mechanical section of the article.

(3)Completed, I am pasting in the inline citation from Toleman for the first formula on entropy as suggested by J-heald.

(4)First stage now complete,These changes being made, my work will be done with the quantum mechanical section, and I also plan to leave the first paragraph of the article alone for a while to let these changes cool down for a while.

(5) I would then like to reconstruct the section on the original Boltzmann H theorem along the lines as it was developed by Toleman, providing the proper inline citations. With a note about the formula offered by Rief.

 * 5(a) My first step will be to copy formulas 47.5 to 47.9 found in Toleman page 135.

Toleman is pretty good about tracing the historical development of H theorem. I plan on making it clear that this is Toleman's development of the concept, leaving any parts of Boltzman's original formulation, not covered by Toleman a bow for another Ulysses. The two developments are close but the extent that Boltzman's development differs from Toleman's so far I have only Toleman's account.

I now have all the fomulas i wanted to add to the article except for one that I am still working on the proper math tags for.

See the really ugly period at the start of the lower part of the formula that I used to get the equals signs to line up????

$$\gamma \,$$

$$H= \sum( n_i \log n_i - n_i \log \delta v_\gamma)$$

$$.\,\,\,\,\,= \sum n_i \log n_i + const$$

I plan on changing the formula current formula for H per unit volume, to make it more in line with the format and definitions of Reif with the appropriate inline citations. Or possibly doing away with it all together? But this would require more discussion. Can anybody provide an inline source citation for this formula?

(6)This will leave the article on H-theorem with still more work to do, but I feel like maybe it will be someone else's turn to take it from there for a while, and I plan on a cooling off period where I might participate in discussion, but not do any more editing of the article for a while. Hobojaks (talk) 20:36, 28 February 2009 (UTC)

 * No time now, but I'll try and comment in more detail on Monday. Jheald (talk) 11:28, 1 March 2009 (UTC)

Icky notation
I found things here that look like this:
 * ναβ(pβ-pα)

How uncouth.

I changed that to this:
 * ναβ(pβ − pα)

Note: In non-TeX math notation,
 * variables are to be italicized; parentheses and digits are NOT;
 * a minus sign is not a stubby little hyphen;
 * binary operators minus, plus, equals, etc. are preceded and followed by a space (don't worry about that in TeX; the software does it automatically); with binary operators I make the space non-breakable. (Minus and plus as unary operators are not followed by a space; thus +5 or −5 is correct.)

See Manual of Style (mathematics).

Also:
 * $$ \int f(x)\,dx = g(x) + \text{constant} \, $$
 * $$ \int f(x)\,dx = g(x) + \text{constant} \, $$

is correct, but
 * $$ \int f(x)\,dx = g(x) + constant \, $$
 * $$ \int f(x)\,dx = g(x) + constant \, $$

is wrong. "Constant" should be set in text mode, not left to get italicized as if the letters were variables. This also affects spacing in some contexts. Michael Hardy (talk) 18:54, 2 March 2009 (UTC)

 * I feel like I have been blessed by the math tag gods here!!!

 * You definitely made the formulas look a lot better. I will need study your techniques.  I am still mastering math tags.

 * The double bar over the H however it seems to me is very important. Taking it off comes at the expense having an equation from a verifiable source.

 * The double bar shows that the quantity we are talking about is an average over an ensembly, and that it is different from the other quantity H used in other sections of the article.

The "Criticism" section is complete nonsense
I am not sure who is the "source" being cited but the criticism clearly shows that its author has zero understanding for the proof presented in the article - and zero understanding for thermodynamics in general.

1) It's the very point of the proof that one divides the evolution into infinitesimal steps that are long enough that the "thermalization" occurs in the interval, and it produces nonzero probabilities for indistinguishable microstates. On the other hand, because this time can still be essentially arbitrarily short for macroscopic systems, the first-order perturbation theory becomes actually exact, so there is no error introduced by the first-order approximation of the Fermi's rule. At any rate, even if a higher-order corrected rule were used instead, one could still prove the inequality.

2) The derivation clearly talks about the probabilities of all possible microstates of the system. It makes no assumption about the number of "particles" or other degrees of freedom that describe the system. So in this sense, the derivation is absolutely exact and surely doesn't neglect any interactions. Only the "critic" is introducing some assumptions about the number of particles and the organization of the Hilbert space as a tensor product. The proof is doing nothing of the sort and is completely general in this sense.

3) It's completely absurd that an isolated system with many (N) particles will "sit in one microstate". Quite on the contrary, it will try to evolve into an equal mixture of completely all microstates with equal probabilities. That's what the proof shows - and what every sane person knows from the 2nd law of thermodynamics and everyday life, anyway.--Lumidek (talk) 09:27, 3 April 2009 (UTC)

I have to agree with the absurdity of this critique. Even if the case can be advanced for the potential invalidity of the H-theorem proof, it must be done under what most would consider rather extreme assumptions. Contrary to the criticism of its applicability, the H-theorem assumes rather mundane conditions, e.g. non interacting particles. Despite what the critic states, non-interaction represents most gases under "ordinary" conditions to an excellent degree for most applications.

While it is possible to prepare states that violate this theorem (e.g. Jaynes, 1971), they are systems which violate the assumptions of the theory, specifically with respect to the strength of potentials. This is not necessarily the case in N-body quantum systems, since even these systems may be treated as systems of N non interacting quantum particles, with successive perturbations (in the form of potentials) approaching the "true" system. The H-theorem will be perfectly valid for this system provided the potentials are sufficiently weak. It should be noted that a system can always be placed in a state that will violate the H-theorem, even in the absence of potentials. What is physically important is that the number of accessible states that will continue to violate the H-theorem as the system evolves decreases with exponential rapidity. For macroscopic systems this is essentially immediate, even if the initial system was H-theorem violating.

This section is out of place in this article, except perhaps as a note linking to another page, if the critic should like to create it, that dicusses scenarios in which the H-theorem is violated, which would necessarily be limited to those cases which strongly violate the assumptions supporting the theory. 68.19.49.85 (talk) 17:28, 14 October 2009 (UTC)

Terribly written article!
1) If Boltzmann proved the H-theorem, why in the world does the article start off with the quantum version of it? First the classical treatment should be given, followed by the quantum version.

2) The article says to look up the Wikipedia entry on Shannon's information entropy in order to better understand the definition of H. This is ridiculous! The H-theorem article should not only be self-contained, but it should be able to explain the H-theorems's foundations better than any other article, since after all, it's about the H-theorem!

3) There are misplaced interjections, such as mentioning "a recent controversy called the Black hole information paradox." at the end of the Quantum mechanical H-theorem section, and a discussion about Loschmidt's paradox and molecular chaos at the end of the Boltzmann's H-theorem section. These should be discussed appropriately in the Analysis section or in their own section.

4) The Analysis section quotes various researchers without references and makes a personal attack on Gull in the paragraph "(It may be interesting ...". Overall it reads like an incoherent rant and rambling.

5) The article is full of sentences devoid of any information, like: "This has led to much discussion." "and thus a better feel for the meaning of H." " something must be wrong" " and therefore begs the question." (even linking to begs the question) "But this would not be very interesting." "With such an assumption, one moves firmly into the domain of predictive physics: if the assumption goes wrong, it may produce predictions which are systematically and reproducibly wrong." — Preceding unsigned comment added by Michael assis (talk • contribs) 20:32, 10 November 2012 (UTC)

Isn't the introduction wrong?
″In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to increase in the quantity H (defined below) in a nearly-ideal gas of molecules.″

Shouldn't the H quantity increase? Also

"As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics."

If I'm not wrong it should be noted somewhere that H should be the negative entropy, because it leads to a lot of confusion otherwise (also considering that in many contexts the symbol H represents the common entropy). Correct me if I'm wrong, I'm not an expert on the subject.

maioenrico — Preceding unsigned comment added by 79.45.212.156 (talk) 15:00, 13 December 2015 (UTC)

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Poincaré's recurrence theorem
This section starts with the statement: "In 1896, Ernst Zermelo noted a further problem with the H theorem, which was that if the system's H is at any time not a minimum, then by Poincaré recurrence, the non-minimal H must recur (though after some extremely long time)."

This statement does not have a citation and more specifically there is no reference for the 1896 article by Zermalo.

Also note that this paper by Poincaré in 1893 does discuss the implications of the recurrence theorem for the second law of thermodynamics.

WhiteBeard120 (talk) 01:07, 24 August 2021 (UTC)

 * Stephen Brush (last column p. 45 to first column page 46) refers to the articles by Poincaré and Zermalo and indicates Zermalo was unaware of Poincaré's priority.

 * WhiteBeard120 (talk) 01:25, 29 August 2021 (UTC)

title: Talk:H-theorem


text:
List of Whaling Walls

This is a list of Whaling Walls, which are large outdoor murals by the American artist Robert Wyland (b. 1956), featuring images of life-size gray whales, breaching humpback whales, blue whales, and other sea life. Whaling Walls (a pun on the Wailing Wall) are created by invitation of the communities, institutions, and building owners of the structures on which they are painted. His first mural was created in 1981, and Wyland's 100th Whaling Wall was painted in Beijing in 2008.

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

title: List of Whaling Walls


text:
Jetfire

Jetfire is the name of several fictional characters from the Transformers franchise. He is almost always depicted as an Autobot with flight capabilities and a jet or space shuttle as an alternate mode. In some continuities, he is a former Decepticon.

Transformers: Generation 1
In the many stories of Jetfire (who was referred to as Skyfire in the TV series), told through the numerous Generation 1 continuities, there is one constant aspect—an early affiliation with the Decepticons, which has served only to convince him to side with the Autobots. Jetfire's dedication to the Autobot cause is matched only by his devotion to scientific and technological advancement. He believes this is the only way victory over the Decepticons can be achieved. It is this overriding belief that tempers his bravado in battle. Nevertheless, he is often one of the most eager Autobots to plunge into combat, and his position as one of the fastest usually means he is the first to do so. Jetfire is created from the same mold as the VF-1S Super Valkyrie from the Macross series (see Toys), including the VF-1S's Gun pod which is described as a laser on Jetfire's technical specifications. He uses a photon missile launcher in robot mode.

Animated series
On Cybertron before the war between the Autobots and Decepticons, Skyfire was a scientist and explorer working with Starscream. Together, they investigated an uncharted planet, actually a prehistoric Earth, where they failed to find any signs of intelligent life. Skyfire wished to scrutinize the planet further, and moving in close enough to the planet, a polar wind storm swept him up and buried him beneath the Arctic ice. Starscream searched for his friend, but was unable to locate him and returned to Cybertron alone.

Millions of years later, in 1984, the Decepticons discovered the frozen Skyfire, while draining heat energy from the Earth's core and reactivated him. Reunited with his old friend, Starscream, Skyfire joined the Decepticon ranks. When the Autobots arrived, Skyfire engaged them in battle, and then rescued Sparkplug and Spike Witwicky when they became stranded on an ice floe. Unknowingly, he took the two to Megatron under the impression that he and the other Decepticons valued human life, but when Megatron took them as prisoners, Skyfire started to question his allegiance. When Starscream ordered him to destroy the captured Autobot search party, he refused, and Starscream turned his weapons on him, leaving him heavily damaged. Repaired by Ratchet, he joined the Autobots and engaged in a dogfight with Starscream which ended when he sacrificed himself to stop the core drain, burying himself in ice once again in the process.

A short time later, however, Skyfire was recovered by Wheeljack and Sideswipe, and immediately participated in an attack on the Decepticons in Peru, where the evil robots were once again attempting to use the Earth's core energy for their own means. Skyfire was almost permitted to destroy the villains' new weapon by Thundercracker, but was then blasted by Starscream (who attempted to blast Thundercracker) and repaired with some difficulty by Spike.

Skyfire would go on to make semi-regular appearances in the immediate future, helping the Autobots evacuate their base when the volcano it was embedded in became active, and flying a squad of troops to battle the Insecticons, Skyfire appeared in a few more episodes, but slowly disappeared from the cartoon, due to legal issues.

Skyfire's animation model made infrequent appearances in the third season, making its final appearance in "Dark Awakening" after being shot down by Quintessons in a space battle.

Books
Skyfire was featured in the 1985 audio and book adventure Satellite of Doom. His appearance matched his animated form, not the toy. During the story, Skyfire is killed.

Skyfire appeared in the audio and book adventure When Continents Collide.

Devil's Due Publishing
Jetfire would also appear in the third G.I. Joe/Transformers crossover from Devil's Due Publishing. He was present with the other Autobots at the Capital City peace celebrations, battling Reflector, but was ordered off by Optimus Prime. He was later seen as part of the combined Autobot/G.I. Joe force attempting to rescue Optimus Prime.

Dreamwave Productions
In Dreamwave's 21st-century re-imagining of the Generation 1 universe, Jetfire was once again presented as Starscream's friend before the Great War started. As the war broke out, Jetfire was slow to choose an allegiance, eventually siding with the Autobots. Despite the fact that he even remained with the Autobots when Optimus Prime and Megatron vanished in an early space bridge experiment and the factions splintered into smaller sub-groups, his original hesitance caused his Autobot allies to regard him with a certain degree of mistrust. Grimlock in particular bore a fierce grudge against him for an unspecified incident involving a mind-controlling cerebro-shell and was perfectly ready to believe that he had betrayed the Autobots when he arranged a meeting with current Decepticon leader Shockwave. Jetfire was among the Transformers kidnapped by the ancient Cybertronian called the Fallen, who planned to use the genetic potential in his spark to awaken Primus, but he was freed by Grimlock, putting the grudge to rest.

Prime and Megatron subsequently returned to Cybertron, but when they and their elite crews were lost aboard the Ark, Jetfire was part of a mission to find them, along with Omega Supreme and the Micromasters Countdown and Groundshaker. When a lead emerged in the form of a beacon from the Sol system, Jetfire and Omega split off from the team (who went on to investigate Decepticon attacks on other planets) and headed off after the signal. The duo entered stasis for the lengthy trip, with Jetfire eventually awakening millions of years later as their craft approached Earth. Before Jetfire could bring Omega back online, however, their ship was attacked by Scourge and crashed in the Arctic, where shrapnel from it killed a pod of whales. Jetfire ejected from the ship before impact and managed to seal Scourge in a booby-trapped stasis pod, but an avalanche buried both of them in ice.

At an ill-defined point in time, the Decepticons discovered Jetfire and brought the slab of ice containing him back to their underwater base. Upon returning from a trip to Cybertron with fresh plans of conquest, Starscream thawed Jetfire out to aid in repelling the maniacal Sunstorm, a clone of himself that Shockwave had created, but which had gone insane. Deducing Sunstorm's clone nature, Jetfire jury-rigged a power siphon to de-energise him, and then reactivated Omega Supreme to battle him. To save his own skin from Autobot retribution, however, Starscream had a change of heart and saved Sunstorm, who led him to a mysterious underground energy reservoir that Sunstorm intended to use to give Starscream powers like his own. Yet another double-cross by Starscream saw Sunstorm immersed in the liquid as well, and it began to destroy him from within as Jetfire engaged him in battle, leading him out into space where he exploded, apparently taking Jetfire with him.

Classicverse
In the Fun Publications Classicverse stories Optimus Prime has returned to Earth commanding Bumblebee, Cliffjumper, Grimlock, Jetfire, Mirage and Rodimus (formerly Hot Rod).

In the story Crossing Over, Jetfire was among the Autobot troops of Optimus Prime who responded to the sighting of Megatron and arrived in time to save the dimensional traveling Autobot Skyfall from Megatron's wraith.

In At Fight's End, Dirge, Ramjet, and Thrust are under the orders of Megatron. The city was defended by Ironhide, Jetfire, Optimus Prime and Sunstreaker.

IDW Publishing
Jetfire was presented as a technician and computer expert, who ran field ops during the battle of Thunderhead Pass trying to find a weakness in Thunderwing that could allow the Autobot-Decepticon army to defeat him. Many years later, he and the Technobots served as a scientific surveillance team orbiting a devastated Cybertron, monitoring it for any signs of life. The discovery of an energy spike caused Jetfire to lead the team down to the planet, where they were assaulted and captured by a team of Decepticon cultists who worshipped Thunderwing. Once freed by Optimus Prime and the Wreckers, his skills at decrypting Bludgeon's computer files uncovered an exploitable weakness in Thunderwing's new power source, allowing Prime to eventually defeat him, and uncovered Shockwave's Energon-seeding plan Regenesis. His appearance is based on the recent redesign of the character seen in the Transformers Classics toy line. He was also mentioned in Transformers: Escalation during a communication between Optimus Prime and him.

Marvel Comics
Jetfire was constructed by Shockwave on Earth to be one of his new Decepticon troops, given life through the powers of the Creation Matrix, tapped from the captive Autobot leader, Optimus Prime. However, before Shockwave could accomplish this, Prime transferred the Matrix into the mind of the Autobots' human ally, Buster Witwicky. Shockwave programmed Jetfire's lifeless shell to recover Buster, but Buster was able to use the Matrix to disassemble Jetfire before he could accomplish his goal. Buster then reconstructed Jetfire and used him to rescue Optimus Prime, who infused Jetfire with true life.

Immediately after this — in the UK's sister Transformers comic series, which interspliced its own original material between reprints of the US Marvel title;— Jetfire participated in the "Dinobot Hunt", helping to track down the rogue Dinobots, who were running wild across America. Still bearing the Decepticon insignia Shockwave had stamped him with, Jetfire was not trusted by Ironhide until he saved him from the deranged Slag, proving his Autobot loyalty.

Subsequently, in the US title, he underwent the Rite of Autobrand and was branded with the Autobot insignia at last.

Jetfire went on to perform few significant actions in the future (although he did serve as the Autobots' acting leader against Galvatron in the Target:2006 storyline), but was clearly thoroughly accepted into the Autobots, as he was one of the small number of voices heard when a new Autobot leader had to be chosen, and Dinobot leader Grimlock was elected.

A story called The Gift in issue 93 of the Marvel UK comics explored Jetfire's problems fitting in with the other Autobots. Wheeljack informed Optimus Prime of a newscast where they learned the Decepticons had taken over a NASA space monitoring facility near the Ark. Prowl and Trailbreaker, with Jetfire as backup engaged the Decepticons Soundwave, Kickback and Dirge as the Decepticons attempted to contact Cybertron with the facility's deep space radio equipment. Although Prowl ordered Jetfire to stop Soundwave from sending his message, Jetfire ignored the order to help save Prowl from Kickback's attack. With the transmission sent the Decepticons retreated victorious. Jetfire then accompanied Jazz to a Blackrock fuel plant to oversee the creation of more fuel for the Autobots. The plant was attacked by Decepticons Thrust and Bombshell. Although Jetfire was able to put out a fire at the plant before it exploded, he blamed himself for being slow to react. Jetfire then visited Buster Witwicky on Christmas Eve and told him of his troubles of not fitting in with the Cybertronian-made Autobots. Buster encouraged the young Autobot by telling him he's the first of a new generation of Earth-made Autobots and he should be proud of what he is.

In issue #27 (US), "King of the Hill!", Perceptor summoned his fellow Autobots Blaster, Hot Spot, Jetfire, Omega Supreme, Ratchet and Silverbolt in order to decide who should take leadership of the Autobots. After an attack by the giant Decepticon Trypticon the leader was chosen - Grimlock.

Sometime later, Jetfire was among the Transformers who attempted to defend New York City from the cosmically-powered Starscream, only to be deactivated alongside everyone else. Unlike most of Starscream's victims, there was no indication that he was revived through the power of nucleon.

Games
The Robots in Disguise Classic line appeared in a simple Flash-based video game on the Hasbro website called Transformers Battle Circuit. In this one-on-one fighting game, you press the right and left arrow keys to try to overpower your opponent. In the game you can play Rodimus, Bumblebee, Grimlock, Jetfire, Starscream, Astrotrain, Trypticon or Menasor. Optimus Prime and Megatron each appear as the boss you must defeat to win the game.

He also featured as a playable character in Glu's android game: Transformers G1 - Awakening

Other media
Marge Simpson appeared as Skyfire in one opening sequence to the Simpsons alongside the rest of the Simpson family rendered as Autobots.

Skyfire briefly appears among the characters in Re-Unification, the 2010 TFcon voice actor play prelude comic.

Toys

 * Generation 1 Jetfire (1985)
 * The first two years of Transformers toys were figures taken from older Japanese toylines, primarily Takara's Diaclone and Microman lines. 1985, however, saw several figures reused from lines created by Takatoku Toys, of which Jetfire was one — that of the VF-1S Super Valkyrie Fighter from the Macross series. This figure was one of the most articulated of the early Transformer toys, featuring fully poseable shoulder, hip, elbow and knee joints, and even poseable sacroiliac joints. The instruction manual for the toy even included the GERWALK mode designed for the Macross version of the toy, which was used in that animated series, and seen briefly in the Transformers season 2 episode "The Day of the Machines".
 * Problems over the Jetfire toy began when Bandai absorbed Takatoku Toys, and Macross regained popularity, leading to Bandai's desire to reproduce the Valkyrie toy themselves. This led to problems for Takara when they imported the Transformers toyline — although Hasbro was able to market the Jetfire toy in their markets, Takara was not, nor could they promote it via the animated series, since the mold was owned by their main competitor, and therefore, it was viewed as potential free advertising for Takatoku (this issue also prevented the Deluxe Vehicles, Deluxe Insecticons, Omega Supreme, and Sky Lynx from being released in Japan, though after Takara merged with Tomy, the latter two were finally released in Japan). Although an animation model had been created for Jetfire based on the appearance of the toy (which could be seen in the original toy commercial advertising the figure), this was quickly abandoned and completely redesigned so as to no longer resemble the Valkyrie. This was the design that went on to feature in the comics and cartoons.
 * Jetfire only saw a few American production runs, as the show the original toy was based upon, The Super Dimension Fortress Macross, was exported to America to become the first third of Robotech. Ironically, since Hasbro released Jetfire first, there was never a U.S. release of an authentic transforming version of the toy for Robotech, even though the design was the series' most recognizable and popular mecha. As with other pre-Robotech borrowings from Macross (for instance, BattleTech), the licensing situation for the toy became murky with two different companies (Big West and Tatsunoko Production) asserting exclusive rights to license Macross merchandise outside Japan. Due to these legal issues, Jetfire has not been among the Transformers toys reissued in the 21st century, instead being offered as part of the War For Cybertron: Siege toyline in his cartoon/comic design.
 * This toy is patented in the U.S. as patent number D287037.

 * Generation 2 Cyberjet Jetfire (1995)
 * The first new Jetfire in a decade was a member of the Cyberjets, highly poseable, ball-jointed jets with pressure-activated launching missiles. A repaint of the Decepticon figure released at the same time named Hooligan -- and consequently erroneously decorated with Decepticon symbols -- this figure bore some physical resemblance to his original (unarmored) self, although his color scheme and missile launcher arm drew attention away from his familiar shape. His tech spec bio made it clear that this was still the same Jetfire as before. Cyberjet Jetfire could be partially transformed into a forward-kneed "gerwalk" mode, but his rear wings and tail made the figure too top-heavy to stand upright for very long.

 * Robot Masters R-Blade (2004)
 * Cyberjet Jetfire figure was redecoed in 2004 for the Japanese-exclusive Transformers: Robot Masters toyline as R-Blade, in a red, white and black color scheme that was a direct homage to the original Jetfire. The bio of this figure specifically noted that Jetfire was the leader of the Cyberjets, although the original figure's bio made no mention of it. R-Blade comes with the missile weapon as a sonic lance and a flare gun.

 * Titanium 6 inch Jetfire (2006)
 * Released in the second wave of the die-cast metal Transformers: Titanium line, this 6" version of Jetfire is based on his Cybertronian mode from Dreamwave's War Within comic book series.

 * Classics Voyager Jetfire (2007)
 * Part of the second wave of releases for the Transformers Classics toy line, this incarnation of Jetfire has a removable booster pack and helmet; with them attached (and excluding the translucent blue missiles), the toy looks much like the Macross (Super) Valkyrie-based original. Without them, he is closer to Skyfire's appearance on the Generation 1 cartoon. His double-barreled rifle was also made to resemble Skyfire's weapon from the cartoon. Some fans have also found a sort of "hidden" mode with the Classics figure. Due to the toy's unusual hip design, it can be configured into a Gerwalk-like mode, although no official public documentation by Hasbro, on the website or instruction sheet, specifies this. Without armor, Jetfire's vehicle mode resembles an F-14 Tomcat, with exhaust design elements inspired by the F-22 Raptor.
 * A printing error on the back of the Classic Grimlock box used Jetfire's picture as one of his co-sells, but listed him as the Decepticon Astrotrain.
 * This toy was remolded into the BotCon 2007 exclusive Timelines Dreadwind and the 2008 Universe Series Tread Bolt.

 * Classics Legends Jetfire (2007)
 * First seen at Botcon 2006, the Legends Jetfire is a repaint of Cybertron Legends Thundercracker in the traditional colors of Jetfire.
 * This version of Jetfire turns into an SU-27 Flanker jet.

 * Henkei! Henkei! C-06 Voyager Cybertron Skyfire (2008)
 * The Japanese version of the Classics Voyager figure by Takara Tomy is virtually identical to the Hasbro version.

 * Gentei! Gentei! Voyager Dark Skyfire (2009)
 * Exclusive to Toy Hobby Market in Japan, this is a dark gray/purple redeco of Classics Voyager Jetfire as a Decepticon.

 * Transformers Kabaya Gum Skyfire (2010)
 * Part of Wave 2 of Kabaya's Transformers candy toy line. The package comes with an easy-to-assemble robot kit and a stick of gum. The Jetfire toy in this line is a simplified version of the Universe/Henkei figure.

 * Generations Leader Jetfire (2014)
 * An all-new mold of Jetfire released as part of the Transformers franchise's 30th anniversary offerings. The figure incorporates design elements of the original 1984 toy and Skyfire's animation art.

Transformers: Robots in Disguise
In Transformers: Robots in Disguise, Skyfire is as loyal to devotion to Megatron, in contrast to his wing-mech Wind Sheer. The 2001 Robots in Disguise Deluxe Skyfire w/ Tow-Line included a Jetfire as a redeco of the Machine Wars Skywarp/Thundercracker mold. Skyfire transforms from a Dassault Rafale fighter jet to robot mode with a single-step, spring-loaded transformation. The two halves of his rifle store in his lower legs in jet mode. He was only available in a Deluxe-level two-pack with Tow-Line. This mold was also used to make Beast Wars II Dirge, Robot Masters Wingstun and BotCon 2006 exclusive Darkside Waspinator.

Unicron trilogy
In Transformers: Armada, Jetfire serves as Optimus Prime's second-in-command, with a cheerful personality that helps to bridge the distance between Prime as a leader and his troops. The friendly nature that keeps him popular amongst the Autobots hides a strong sense of intelligent judgment that has saved his team from numerous predicaments and means that he will even speak up and tell Prime that he is wrong to his face.

Transformers: Armada
In this series, he is very boastful. When Optimus Prime led a small force to Earth to investigate the Mini-Con signal emanating from that world, Jetfire was left in charge on Cybertron, but eventually later departed the planet to join his commander on Earth. Arriving shortly after the Decepticon tactician Thrust, Jetfire scanned an Earthen space shuttle upon approach to the planet and burst onto the scene in the middle of a battle, his energetic and unexpected arrival completely throwing off Thrust's meticulous plan and allowing the Autobots to claim victory. When Thrust arranged the next Decepticon attack on the Autobots, Jetfire once again proved to be the monkey wrench in his plan when he and Optimus Prime revealed their ability to combine, once again foiling the villain's schemes. Although, Optimus Prime said "Jet Convoy" the first time they combined, later in the series he referred to it as Jet Optimus.

Jetfire's unique space-flight abilities make him a distinct asset to the Autobot forces, allowing them to recover a Mini-Con from Mars. He journeys there together with Starscream who had joined the Autobots at that time. Jetfire is displeased that the turncoat Decepticon will keep his company, but he cannot do anything about it, for Starscream simply takes off the first and leaves him behind. So Jetfire has only alternative to follow "this brainless robot" reluctantly. On the way to Mars, however, he loses sight of Starscream and finds him only with the aid of the Air Defense Mini-Con Team. He invites Starscream to look for the Mini-Con together, but the latter refuses. Then Jetfire arrests and shackles Starscream for insubordination. While Jetfire tows his prisoner back to Earth, Megatron and Tidal Wave attack them. But, despite their disagreement, Jetfire and Starscream prove to be capable of acting as a team. So they succeed in resisting the enemy and in rescuing the Mini-Con.

It is noteworthy that after Starscream refuses his help, though being seriously damaged, Jetfire remarks that he is "stubborn as usual"; supposedly, he had already gotten to know Starscream's nature well enough.

When Optimus Prime dies at the hands of the Decepticon super-weapon, the Hydra Cannon, Jetfire steps down to allow Hot Shot to assume command, retaining his secondary position even when Prime was returned to life by the power of the Mini-Cons. Jetfire goes on to participate in the "Unicron Battles," when the planet-eating giant robot Unicron attacks Cybertron and returns the Autobots' human allies Rad, Carlos, and Alexis to Earth after the battle is won.

Transformers: Energon
Over the ensuing decade, Jetfire (now called Skyfire in Japan) received an upgrade into a new body, and received the Spark of Combination from Primus, allowing him to combine with other Autobots, most frequently the rookie trooper Ironhide, who he had to carefully train and walk through the combination process. Despite his external changes, however, Jetfire remained consistent in personality and outlook, always ready with a witty remark to keep the mood light even in the middle of a pitched battle. He is once again, the second-in-command of the Autobots.

When the resurrected Unicron came under the control of Megatron, Primus used his powers to permanently super-charge some of the Autobots, Jetfire included, recoloring their armor. The resultant battle saw Unicron's body destroyed, but his spark endured and possessed Megatron — now Galvatron - who grew to colossal size. To combat the giant villain, Jetfire, and the Autobots took their Spark of Combination to the ultimate extreme, transforming their bodies into pure energy and merging with Optimus Prime, enlarging him to similar proportions and allowing him to battle Galvatron directly. Ironically it was Galvatron who was ultimately the instrument of Unicron's defeat when he plunged himself into an energon sun created by Primus in order to stop Unicron from taking over his body permanently.

Transformers: Cybertron
In order to recuperate after the stresses of the final battle against Unicron, Jetfire (Dreadrock in Japan, a new character there, not the same as the Jetfire from Superlink, but is still the Autobot's second-in-command) took some time out to vacation of the planet of Nebulos, where he inadvertently picked up the local accent (resembling Earthen Australian). His relaxation was brought to an end, however, when Primus's energon sun collapsed in on itself, forming a gigantic black hole that threatened the safety of Cybertron.

Returning to the planet, Jetfire helped the Autobots there evacuate, relocating once more to Earth, where he suggested the Autobots revisit the idea of taking on Earthly vehicle alternate modes to hide from the populace, adopting for himself a new cargo plane alternate mode. He went on to develop a rivalry with Decepticon Thundercracker over who was the superior flyer. Jetfire was Optimus Prime's second-in-command in this series and was rather cocky. Jetfire participated in many of the battles on Earth, Cybertron, and Giant Planet.

In the episode "Warp", It is revealed that he has a fear of needles (trypanophobia).

In the episode "Unfinished", when the Autobots attempted to use a gigantic rocket to move the Animatros back into its orbit, Galvatron attacked and damaged the rocket. The jungle planet threatened to crash into Cybertron. Scourge, the Autobots, the former Decepticons, and their allies from the various planets were able to combine their strength and move the rocket back into place.

After the threat of the black hole was thwarted, he was appointed leader of Cybertron in Optimus Prime's absence.

Jetfire wields two guns, and is able to generate twin whirlwinds from his shoulders. His Earth-type Cyber Key activates twin missiles in his back. Later, the Jetfire toy was repainted as a Decepticon named Sky Shadow. His bio says that Sky Shadow is actually an undercover Jetfire.

Transformers: Energon
Over the following decade, Jetfire retained his position as Autobot's second-in-command through the Autobot/Decepticon alliance. Unicron's threat, however, had not been ended, as was proven when the Terrorcons; dissident Decepticons given new powers through Unicron's intermediary agent, Alpha Quintesson; attacked the AlterEnergy research facility on Earth and Jetfire, now equipped with the Spark of Combination, joined the other Autobots in defending it and its human occupants.

The Terrorcon threat underwent sudden, horrific multiplication when they were cloned through Unicron's power, and massive swarms of them assaulted key cities across Earth. Jetfire petitioned the High Council to allow more troops and Energon to be dedicated to Earth, and it was only through the efforts of council member Avalon that his appeal was accepted. A large strike force under Jetfire's command was assembled and sent to Earth, with Jetfire taking a portion of the team (Bulkhead, Cliffjumper, Landquake, Perceptor and Tow-Line) to Los Angeles. Despite fighting a tough battle, it was soon apparent that the Autobots were not going to win, until Megatron; reborn in a vastly powerful new body; came blasting onto the scene and shattered the Terrorcon forces, allowing Autobot victory.

IDW Publishing
IDW's Transformers Collectors Club exclusive comic story, "Revelations Part 6", is set after the defeat of Galvatron but before Optimus Prime's mission to start a new Space Bridge project. In this story the Autobots from the Fun Publications stories (Robots in Disguise Optimus Prime, Ultra Magnus, Sentinel Maximus, Downshift, Perceptor, Alpha Trion, Over-Run, Anti-Blaze, Checkpoint, and Scythe) meet the Autobots from the animated series (Cybertron Optimus Prime, Jetfire, Override, Scattorshot, Red Alert, Hot Shot, Lori, Bud, and Coby Hansen) and thank each other and remembering those who were lost in the battles.

Toys

 * Armada Jetfire with Comettor (2002)
 * Jetfire transforms into a space shuttle; the landing gear becomes a shield for his robot mode, while one of the three thrusters becomes a large gun with an electronic engine and laser noises. Jetfire is packaged with the Mini-Con Comettor, which transforms into a lunar rover and mounts as landing gear for Jetfire in shuttle mode. When plugged into the gun/thruster, Comettor triggers two spring-loaded tail fins to pop out and switches the laser noise to a "5-4-3-2-1" countdown. When plugged into the shuttle's wings, Comettor causes two bombs to drop, which can also be stored in other inactive slots. Jetfire can also transform into a set of legs, atop which Optimus Prime's super mode torso can attach, forming Jet Optimus (Jet Convoy in Japan).
 * A special Target store exclusive bonus pack of Armada Jetfire with Commetor came with the Space Team Mini-Cons Payload, Skyblast, and Astroscope.
 * According to the Transformers Collectors Club magazine, the vehicle mode of this Jetfire is inspired by the X-71 Shuttle from the 1998 film Armageddon.

 * Armada Powerlinx Jetfire with Comettor (2003)
 * A blue and white redeco of the Armada Jetfire figure, representing Jetfire in his enhanced body, as seen in the Transformers: Armada comic books.
 * A redeco of this mold was intended for release in Transformers: Universe as the Decepticon Spacewarp, but this was canceled. A slightly altered version of this toy was later revived as an exclusive for the Official Transformers Collectors Club, as the classic Decepticon Astrotrain, with a new head sculpt to resemble the character's classic head design.

 * Energon Jetfire (2004)
 * The new Energon incarnation of Jetfire features a spring-loaded missile launcher and undercarriage grabber claws. The figure bears a golden Powerlinx symbol, meaning that it can combine with other figures of the same size, forming either a torso or legs to do so. Connecting the figure with another produces an electronic linking noise, while pushing down on Jetfire's head yields a sped-up version of the classic "transformation" sound. The toy can also link with smaller silver Powerlinx figures, but the results are disproportionate, and not used in the animated series, comics, or the figure's English instructions.

 * Micron Legends Skyfire S (2005)
 * Another blue and white Jetfire redeco, this time of the Energon toy. Released in Japan as "Skyfire S" (the "S" stands for "Sonic"), it represents the character in his upgraded form from the animated series. The toy was also released in Hasbro markets, but as a different character named Overcast, Jetfire's brother.

 * Cybertron Ultra Jetfire (2005)
 * The new Cybertron incarnation of Jetfire is armed with twin firing missile launchers, which mount under his wings in plane mode. Pressing on the rear of his tail engines activates an electronic engine noise, while flipping the tail section up changes the noise to a shrill laser blast. Inserting the figure's Earth Cyber Planet Key into the tail section causes a pair of twin guns to pop up, changing the noise once more, into an explosive blast. The toy features some auto-transforming features — by snapping the nosecone into the hips during the transformation into robot mode, two small missile cluster launchers are popped out, while straightening the arms at the elbows automatically extends the fists.
 * Like most toys sold in the Galaxy Force toy line by Takara, then later in the Cybertron toy line by Hasbro, there are small paint differences between the two versions of the toy. The Hasbro version has a code number on the back of his Cyber Key, while the Takara version has no number on his Force Chip.
 * This toy was recolored into 2007 live-action movie Jetstorm.
 * This toy stands 19 centimeters tall in robot mode. In the animated series, Jetfire is depicted as standing 24 feet (or 732 centimeters) tall. This would make this toy 1/39 scale if you base the toy on the size depicted in the show.
 * A real An-225 has a wing span of 8840 centimeters, while this toy has a wingspan of 27 centimeters, making this toy have a scale of about 1/327 of the real world vehicle. With the toy robot mode standing 19 centimeters tall, the actual robot mode of this character would stand about 6220 centimeters (204 feet) tall.

 * Cybertron Burger King Jetfire (2005)
 * A small simple version of Cybertron Jetfire was sold with Burger King kids' meals.

 * Cybertron Legends Jetfire (2006)
 * A small version of the larger Cybertron Jetfire toy, this figure features a simplified transformation scheme that imitates the bigger figure. In 2007 a Target store-exclusive value pack of four Voyager class Cybertron toys was released. It included Jetfire, Megatron, Optimus Prime, and Soundwave. All are identical to their original releases.
 * This toy stands 8.5 centimeters tall in robot mode. In the animated series, Jetfire is depicted as standing 24 feet (or 732 centimeters) tall. This would make this toy a 1/86 scale.
 * Repainted in 2007 as Classic Legends Fireflight (Transformers).

 * Cybertron Ultra Sky Shadow (2006)
 * A recolor of the Cybertron Jetfire figure in tan, black, and maroon, this figure represents Jetfire in a Decepticon guise used for undercover missions. The name is a reference to the Beast Wars Predacon Sky Shadow, whose name Jetfire is found in the Cybertron Archives. Because this recolor was a Hasbro exclusive made after the animated series was already produced in Japan, he did not appear in the television series.

 * Transformable Robot Armor Battleplane (2007)
 * A Chinese-made unofficial toy based on the Legends of Cybertron Jetfire in a larger size and with slightly different colors. Came with an additional rifle accessory. Available at discount stores like Big Lots.

Transformers 3D Battle Card game (2007)
Jetfire is among the characters that first appeared in the 2007 Transformers 3D Battle Card game by Wizards of the Coast. A red and white redeco of movie Starscream, this incarnation of Jetfire is not related to the character in the 2009 film Transformers: Revenge of the Fallen.

Toys

 * Transformers 3D Battle Card Jetfire (2007)
 * An Autobot redeco of the Starscream card. His alternate mode is a jet fighter based on an F-22 Raptor.

Transformers Cinematic Universe
In a USA Today online fan poll following the release of the 2007 live-action film, Jetfire was one of the 10 Transformers that the fans wanted in the sequel, coming in 4th with 11% of the votes.

Jetfire appears in Transformers: Revenge of the Fallen and transforms into a Lockheed SR-71 Blackbird. He is portrayed as a former Decepticon who becomes an Autobot because he did not believe in all the destruction and violence the Decepticons were dedicated to. Originally serving the Fallen, Jetfire is one of the few Transformers to remain on Earth since the dawn of humanity.

According to the biography and statistics published on the Hasbro website, Jetfire is 50 feet tall and his main weapon is a battle-axe. In the film, he also has a rocket launcher. As an emphasis on his old age, he carries a walking stick that transforms into the front landing gear of his jet mode. In the film, he can project hologram clips from the palm of his left hand similar to how Optimus Prime did in the 2007 film through his eyes.

IDW Publishing
Jetfire was spotlighted in Tales of the Fallen issue #3. He was depicted as a member of the Decepticons under the leadership of the Fallen, serving the villain due to being tricked as to believe he was working for Cybertron's benefit. However, when the other Primes confronted the Fallen on Earth, Jetfire realized his mistake and was teleported to an unknown location. Jetfire fought many other ancient Decepticons there and eventually went into stasis after his victory. He awakened in the mid 20th century and scanned an SR-71 Blackbird before returning to stasis. His Decepticon insignia was unchanged even when he switched sides to the Autobots.

In Defiance issue #4, which is a prequel to the movie series, a younger Jetfire is seen in his Cybertronian mode, traveling the galaxy for star-orbited planets, in a flashback told by the Fallen to Megatron.

Books
In the novel adaptation of Revenge of the Fallen, Jetfire is confronted just after arriving in Egypt by his fellow Decepticon Seeker Ransack. After firing off an ineffective round at Jetfire, Ransack is crushed under Jetfire's foot.

Movie plot
Jetfire is found by Sam Witwicky, Mikaela Banes and Seymour Simmons at the Steven F. Udvar-Hazy Center, an annex of the National Air and Space Museum, after Wheelie pinpoints the general location of the ancient Seeker. Sam reactivates him with an Allspark fragment, waking him up from the stasis lock. After a misunderstanding when the humans saw his Decepticon insignia, Jetfire activates a Space Bridge to teleport Sam and his friends to Egypt, explaining to them the origin of the Primes (who he seems to have a certain type of respect for) and the Matrix of Leadership. Learning of Optimus Prime's existence and death, Jetfire sends them to find the Matrix, which he speculates can be used to revive Optimus (Although it could also be used to power the Fallen's technology).

He later joined the Autobots in battling the Decepticon forces in Egypt, killing the Decepticon weapons expert Mixmaster, before being badly injured by Scorponok. In a final act of sacrifice, he took his own life to enable Optimus to use his parts for an upgrade for his battle with the Fallen.

Games
Jetfire is a playable character in the PS2 and Wii versions of the Transformers: Revenge of the Fallen video game and is in the new downloadable content pack for the PS3 and Xbox 360. He is only playable in multiplayer mode.

He also appeared in the video game Transformers: Rise of the Dark Spark.

Toys
All toys of this character are officially licensed from Lockheed Martin.

 * Revenge of the Fallen Legends Class Jetfire (2009) In September 2008, pictures of a mold for a Legends Class Jetfire appeared online. Jetfire transforms into an SR-71 Blackbird and can also combine with Legends Class Optimus Prime on his back. This toy was seen on the internet in package as a Decepticon in December 2008.
 * Revenge of the Fallen War for the Skies Legends Class Jetfire (2009) A silver redeco of the Legends Class figure. Bundled in a Kmart exclusive Legends gift set with Autobot Blades, Thundercracker and Spinister.
 * Revenge of the Fallen Fast Action Battlers Photon Missile Jetfire (2009) A Deluxe Class-sized figure of Jetfire with simplified transformation for younger children.
 * Revenge of the Fallen Robot Replicas Jetfire (2009) A smaller, non-transforming action figure.
 * Revenge of the Fallen Leader Class Jetfire (2009) A larger version of Jetfire (and the largest of the Leader Class), with MechAlive technology and a more complex transformation procedure. Features electronic lights and sounds, and says "Jetfire's my name." in a Scottish accent. Also combines with the newer Leader Class Optimus Prime.
 * Revenge of the Fallen Jetpower Optimus Prime with Leader Class Jetfire (2009)
 * An Asia-exclusive gift set featuring a black/gold redeco of Jetfire with Buster Optimus Prime.

 * Revenge of the Fallen Leader Class Power Up Optimus Prime Value Pack (2010) A Hasbro Toy Shop exclusive gift set featuring Leader Class Optimus Prime and Jetfire. Unlike the Asia-only gift set, this package features the regular figures and not the Buster Prime or repainted Jetfire variants.
 * Transformers The Victory of The Fallen Legends Class Jetfire (2010) A black/silver redeco of the Legends Class figure. Bundled with Legends Class figures of Optimus Prime, The Fallen, Megatron and Starscream.
 * Dark of the Moon Jetpower Optimus Prime with Leader Class Jetfire (2011) A re-release of the Asia gift set for the DOTM toyline. None of the figures were changed.
 * Age of Extinction Scientist Class G1 Jetfire (2014) A new mold of Jetfire in G1 colors

Transformers: Animated
Concept art for an Animated rendition of Jetfire, as well as Jetstorm, was shown at BotCon 2008, revealing Jetfire to be a yellowish-colored robot and Jetstorm to be a blue-colored robot. He has goggle-like pieces on their foreheads and they both transform into jets. Jetstorm and his brother Jetfire are Autobot twins who have been fitted with technology scanned from Starscream while he was in Elite Guard captivity.

They have the power to create powerful whirlwinds in both robot and jet modes. Jetfire can combine with Jetstorm, forming Safeguard. In their combined vehicle mode they resemble an X-wing fighter from Star Wars. The two are enthusiastic young fighters but do tend to rush into things. He speaks with both the twins' voices simultaneously.

Both Jetfire and Jetstorm are the youngest members of the Elite Guard of all time. Both Jetfire and Jetstorm speak with Russian accents. Apparently, they are Sentinel Prime's soldiers, obeying his every command. The twins' merging into Safeguard is similar to ChoRyuJin of The King of Braves GaoGaiGar.

Animated series
He first appeared in "Where is Thy Sting?". Both he and Jetstorm speak with Russian accents. Apparently they are Sentinel Prime's soldiers, obeying his every command. The two also appear to have a kiddy sense of fun and amusement, as shown when Bumblebee plays a video game against Wasp to determine who is who. They both raise their hands and state that they will play the winner.

Jetfire reappeared in "Five Servos of Doom". Jetstorm wanted Jetfire to scan a picture of him in front of the recently captured Decepticon Blitzwing "for the Femme-bots back home". He then asked how Sentinel Prime captured Blitzwing. He was later seen with Jetfire trying to make the communicator work. He directed Prowl and Jazz to the Elite Guard flagship's brig, where Sentinel had just captured Lugnut. He also appeared with Jetfire in a baseball stadium, where Sentinel was working with Lockdown. Jetstorm combined into Safeguard and helped rescue Sentinel, who was now in the hands of Ramjet. Jetstorm was present when Prowl used Processor Over Matter to lift the rubble of the scoreboard off of him.

In "Predacons Rising", Bumblebee, Jetfire, Jetstorm, Optimus Prime, and Sentinel Prime chase Wasp, but lose him to Swoop while bickering about what to do with him. The group follows them to Blackarachnia's lab, and, in the ensuing battle, Jetstorm and Jetfire hand the Dinobots a crushing defeat. In this episode after following Sentinel's orders, which got him buried headfirst in the sand, Jetfire asks, "Should we be taking notes?" to which Jetstorm replies, "On what not to do?"

Jetfire and his twin appeared in "Decepticon Air", fighting back against the escaped Decepticons captured on Earth.

They appeared again in "This is Why I Hate Machines", surprised to see Ratchet and Captain Fanzone on Cybertron. They reluctantly followed Sentinel's orders to organize a strike against Omega Supreme (containing Megatron, Starscream, and Lugnut), who had recently transwarped above Cybertron.

Toys

 * Animated Deluxe Jetfire and Jetstorm set (2008)
 * A Deluxe Class boxed set of Jetfire and Jetstorm. Both figures transform into jets and can combine into Safeguard.

 * Animated Set G Safeguard (TA-21 Jetfire and TA-22 Jetstorm) (Takara Tomy) (2010)
 * The 2010 Japan release version by Takara Tomy. On this version, Jetfire sports a metallic silver finish, while Jetstorm has blue chrome parts.

Aligned Continuity
Jetfire is a member of the Aerialbots, but does not seem to make up any part of Superion. He was formerly a neutral Scientist until Starscream betrayed him and joined the Decepticons; in retaliation, Jetfire joined the Autobots.

Books
Jetfire appears in the novels Transformers: Exodus and Transformers: Retribution. A former Seeker, Jetfire chooses to side with the Autobots rather than joining the Decepticons along with most of his fellow Seekers and becomes one of a handful of Autobots who are flight capable. He proves to be a valuable asset, and remains behind on Cybertron to aid the Wreckers when the Ark departs. Despite his valiant efforts, some Autobots-notably Wheeljack-continued to doubt his loyalty and suspected that he was a double agent for the Decepticons. Jetfire proved his loyalty by joining a mission under Ultra Magnus to rescue Alpha Trion from Shockwave.

Games
Jetfire is one of the playable Autobots in the 2010 video game Transformers: War for Cybertron, and speaks with an English accent (similar to his film incarnation). In the Decepticon campaign, he starts out as one of Starscream's partners in charge of guarding the dark energon. He also tries to warn Megatron about the deadly effects of dark energon, but his cries fall on deaf ears, as the Decepticon leader immerses himself in it, becoming more powerful. After that Starscream turns his allegiance to Megatron. Jetfire fled the scene, joining the Autobots.

In the Autobot campaign, Jetfire joins Air Raid and Silverbolt in flying in orbit of Cybertron to take down the armed Decepticon orbital station Trypticon, which is preventing Autobot transport ships from leaving the dying planet. The aerial trio enters Trypticon and destroys his cooling systems and plasma reactor, disabling his main weapon. Unfortunately, the attacks are not enough to disable Trypticon, so they enter his core and destroy his transformation cog, forcing him to revert to his true form. Forced to transform into dinosaur mode, Trypticon sets a course toward the Autobot city of Iacon with the intent of decimating it, but the Autobot trio destroys his flight pack, sending him crashing into the planet. This leaves Optimus Prime and his ground-based team with the task of finishing off Trypticon before he lays further waste on Iacon.

Jetfire is playable in the last level of Transformers: Fall of Cybertron. The player's mission as Jetfire is to destroy the Decepticon tow cables and help Jazz knock Bruticus off the Ark.

title: Jetfire


text:
Talk:Red vs. Blue (season 2)

Deletion
This page, as well as the two other "seasons" are fancruft par excellance. This is completely unencyclopedic and it's only existence on Wikipedia should be in the form of a link to a fan-page. --The Grza 06:44, Apr 12, 2005 (UTC)

VfD
On April 14, 2005, this article was nominated for deletion. The result was keep. See Wikipedia:Votes for deletion/Red Vs. Blue episode guide: Season 3 for a record of the discussion. Mindspillage (spill yours?) 16:37, 29 Apr 2005 (UTC)

Episode 36 multiple titles
Episode 36 has at least three titles that I've seen: ''Nut. Doonut, Blunderball and Dummies are Forever''. Which is the most correct? Is it different on the DVD? I have the low quality DivX version, and it is ''Nut. Doonut''. Should a note be made of this?--Drat (Talk) 06:03, 25 February 2006 (UTC)
 * "Nut. Doonut." is the title on the Rooster Teeth website and on the DVD and probably should be considered the primary title. However, I just investigated, and each of the six episode 36 versions downloadable from the Rooster Teeth website shows a different full title on playback (the DivX low-res version now shows, "Dummies Are Forever"). Another one of Rooster Teeth's subtle jokes. Too much information for a footnote, so I put it into a table that I just added. — TKD (Talk) 08:08, 25 February 2006 (UTC)
 * I was incorrect about the low res DivX version. I just assumed. Whoops. But I agree with the choice of primary title.--Drat (Talk) 08:40, 25 February 2006 (UTC)

I'm beginning to wonder if this information is important at all. It feels almost like damned dirty trivia. Would a simple note regarding the existence of multiple titles suffice?--Drat (Talk) 05:33, 30 May 2007 (UTC)

Star Wars reference
Sorry, but I felt that it had to go. According to RT (in one of the season DVD commentaries, probably that of season 3), they said they orchestrated the exodus from Blood Gulch because they didn't know whether that map would be available in Halo 2. So it seems a bit farfetched to suggest that Simmons' line was a conscious reference to Star Wars. — TKD::Talk 20:42, 15 April 2006 (UTC)

Move proposal
Please see Talk:Red vs Blue for discussion. — TKD::Talk 17:34, 26 August 2006 (UTC)

Ep. 28 V2
Why isn't there a summary for this? It may not fit in with the rest of the season but it is a part of season 2.--Darthbalmung 21:20, 12 June 2007 (UTC)
 * It's in the list of special episodes. -- Viewdrix 23:47, 12 June 2007 (UTC)

title: Talk:Red vs. Blue (season 2)


text: User talk:217.43.49.172

title: User talk:217.43.49.172


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Talk:Cerealia

Untitled
What's this one hears about foxes with their brushes alight, set loose in the Circus Maximus? What's the Roman origin of this tale that reminds me of Samson? --Wetman 06:45, 12 Apr 2005 (UTC)

This page is titled incorrectly. This Holiday is correctly spelled Cerialia. you can see this on this page A Dictionary of Greek and Roman Antiquities (1890) —Preceding unsigned comment added by 99.147.247.87 (talk) 23:00, 3 February 2009 (UTC)

I changed the date of the festival to April 11th on the authority of Ovid, Fas. IV, 393.Aldrasto (talk) 09:58, 20 December 2009 (UTC)

Pic not relevant
Getty's description makes clear that although no-one knows precisely what Alma-Tadema meant to depict in terms of Roman festivals, the most likely candidate is one day of several from Flora's festival, which started towards the end of April and continued into May. Or perhaps Maia or Bona dea as a women's goddess. It sure doesn't have much to do with Cerealia. No wheat! No foxes! No matrons! https://www.getty.edu/art/collection/objects/611/lawrence-alma-tadema-spring-dutch-1894/ Haploidavey (talk) 16:07, 30 August 2021 (UTC)

title: Talk:Cerealia


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Rufous-breasted hermit

The rufous-breasted hermit or hairy hermit (Glaucis hirsutus) is a hummingbird that breeds from Panama south to  Bolivia, and on  Trinidad, Tobago and Grenada. It is a widespread and generally common species, though local populations may change in numbers and disappear altogether in marginal habitat.

Taxonomy
The rufous-breasted hermit was formally described in 1788 by the German naturalist Johann Friedrich Gmelin in his revised and expanded edition of Carl Linnaeus's Systema Naturae. He placed it with all the other hummingbirds in the genus Trochilus and coined the binomial name Trochilus hirsutus. Gmelin's description was based on that of the German naturalist Georg Marcgrave in his Historia Naturalis Brasiliae that had been published 140 years earlier in 1648. The rufous-breasted hermit is now placed with two other species in the genus Glaucis that was introduced in 1831 by the German zoologist Friedrich Boie. The genus name is from the Ancient Greek glaukos meaning "blue-grey", "glaucous" or "pale green". The specific epithet hirsutus is Latin meaning "hairy" or "bristled". The type locality is northeast Brazil.

Two subspecies are recognised:
 * G. h. insularum Hellmayr & Seilern, 1913 – Grenada, Trinidad and Tobago
 * G. h. hirsutus (Gmelin, JF, 1788) – Panama and west Colombia through Venezuela and the Guianas to Brazil and north Bolivia

Description
The rufous-breasted hermit is 10.7 cm long and weighs 7 g on average. The bill measures around 3.3 cm and is strongly decurved, long and thin – though compared to the bills of other hummingbirds, it is rather robust. The rufous-breasted hermit has a brownish head, bronze-green upperparts and rufous underparts. The tail has green central feathers and rufous outer feathers, all tipped white. The bill has a yellow lower mandible and a black upper mandible. Sexes are similar, but the male has yellow streaking on the upper mandible, and the female may be slightly duller in plumage. The bill of females is also proportionally a bit shorter (though this is hardly recognizable) and more decurved (which is quite conspicuous in direct comparison).

Males are somewhat more distinct, resembling a barbthroat (Threnetes). They were once described as a distinct species, the "black barbthroat" ("T. grzimeki"). Similarly, the proposed subspecies abrawayae is apparently based on individual variation occurring in adults and not taxonomically distinct either.

The call of this species is a high-pitched sweet.

Behavior and ecology
This hermit inhabits forest undergrowth, often near running water. The rufous-breasted hermit's food is nectar, taken from a variety of understory flowers, and some small invertebrates.

Food and feeding
G. hirsuta has very discriminating feeding habits. It will only visit flowers whose corolla length and curvature precisely matches that of its bill, while most other hummingbirds are far more flexible. Thus, its foodplants are found across almost the entire diversity of angiosperms. Very popular with this bird are Zingiberales, such as Costus scaber (Costaceae), or Heliconia standleyi and Heliconia stricta (Heliconiaceae). Other well-liked foodplants of this hummingbird include Gentianales like Duroia hirsuta, Palicourea lasiantha, Psychotria bahiensis and Psychotria platypoda (Rubiaceae), Lamiales such as Sanchezia peruviana (Acanthaceae) or Drymonia semicordata (Gesneriaceae), and Myrtales like Cuphea melvilla (Lythraceae). Even congeneric plants with flowers of slightly different length and curvature are avoided on the other hand.

Given the difference in bill curvature between males and females, it seems likely that the sexes avoid competing for the same food resource by visiting different plants, but there has been little in-depth study. Whether there has been any coevolution between the hairy hermit and its foodplants is more difficult to determine, but if anything, it seems to be less widespread than it could be presumed. Most plants visited by this hummingbird are also pollinated by less discriminating species. But for some (such as Cuphea melvilla, Psychotria bahiensis and P. platypoda) the hairy hermit seems to be a pollinator of crucial importance, indicating that – though less often than the characteristic bill shape suggests – strong mutualisms between this bird and some of its foodplants do indeed exist.

Breeding
The female rufous-breasted hermit lays two eggs in a small cup nest with a tail, made of rootlets and attached to the underside of a palm, fern or Heliconia leaf one or two meters (3–6 ft) above ground or so. The nests are often near a stream, waterfall or roadside, and are surprisingly easy to find. Incubation is 17 days with 23 more to fledging, and this species may nest up to four times in a season. The male of this aggressive and inquisitive hummingbird helps to build and defend the nest, but does not incubate the eggs. At least regionally (e.g. in Colombia), the species breeds all year.

title: Rufous-breasted hermit