Talk:Equipartition theorem

message: The theorem as stated now in Wikipedia is incomplete because it is valid not only for "kinetic" energy, but for "total" energy.
One possible way of stating the correct theorem is: 
"Each quadratic term in the Hamiltonian contributes with k_B T /2 to the total (kinetic + potential) average energy in the classical limit".
The demonstration is quite easy: see for example page 43 of R. K. Pathria "Statistical Mechanics", Pergamon Press (Oxford 1972). 
Note that wherever in the present Wikipedia artical says "kinetic energy" should be replaced by "total energy".
87.221.5.221 16:07, 15 February 2007 (UTC)
replies: text: Thank you for your kind suggestions, Prof. Franzese.  Hopefully, we improve the article and state the theorem in an even more general form.  Please be patient with us; it may take a few weeks.  Your suggestions would always be welcome. :)  Willow 12:36, 24 March 2007 (UTC)
thread_title: Suggestions

message: Impressive tracking down on the history!
The Waterston date looks like it should be earlier: either 1843 or 1845 or 1851, according to this webpage .
Maxwell and Kelvin's close friend Tait is said to have given "the first proof" of the theorem.  (1886-1892). [But exactly what theorem?]
:Some background on the state of the proposition in the late 1880s here (under "Kinetic theory of gases").  
:But still not quite clear what Tait was supposed by Kelvin to have proved. Jheald 07:39, 24 April 2007 (UTC)
thread_title:  Waterston date 

message: The superscripts "kin", "grav", "pot", etc. should probably be in \mathrm{}. Michael Hardy 03:49, 29 April 2007 (UTC)
replies: text: OK, I'll fix that; thanks for pointing it out! :) Willow 10:10, 29 April 2007 (UTC)
thread_title:  a style detail 

message: As a statistician rather than a physicist, I was puzzled by the (non-Adobe!) p.d.f.s in Fig 2.  Why is the y-axis labelled Probability density (s/m)?  I expect the integral of a pdf (usually) to be unity.  Is this a special notation?  I suggest linking the phrase probability density function in any case.
Sorry: having read further I see that you do finally explain the point under "Derivation for kinetic energies".  Maybe some explanation earlier on would be useful. --NigelG (or Ndsg) | Talk 10:25, 1 May 2007 (UTC)
replies: text: Done. How does it look now? Geometry guy 11:01, 1 May 2007 (UTC)
replies: text: That seems to clear it up!  Thanks. Good luck with the FAC.  --NigelG (or Ndsg) | Talk 18:42, 1 May 2007 (UTC)
thread_title:  Simple question 

message: I didn't think it would be quite so hard to put the examples back in order, but I think I have done it now. I've moved the simplest quadratic energy examples to the first section. These are the examples that the reader needs to know to understand the history. The remaining examples have been combined in one section. I see no reason to call this section "Advanced" (that is just intimidating), but there is much that can be done to make it more friendly. I've done my best to maintain all (non-repetitive) material and links, but I may have made mistakes, since this work was not easy to do, so please check what I have done. I hope my edit summaries are helpful.
I'm done for today, but not in general: the history needs to be revised and the applications section needs to be shortened. Also I would like to be more bold with the general formulation and state it up-front, then derive its implications. The reverse approach just makes it seem more complicated than it is, in my opinion. Geometry guy 00:44, 2 May 2007 (UTC)
replies: text: I think you did a great job.  Maybe the revisions discussed in the above topic could be obviated by simply putting the shortest possible paragraph(s) before or within the current first section, where we would very simply state the general form of the theorem, followed immediately by its quadratic energies form, with only a brief reference to derivations below.  Starting with literally only two equations, with one of them general and one in accessible form, couldn't possibly be confusing to the reader of an article about a theorem, right?  We could even make a pretty box for them.  :)  Gnixon 02:24, 2 May 2007 (UTC)
replies: text: Parenthetical remark to my main comment below:  (I'm not sure using "theorem" is inherently problematic.  Physicists frequently talk about theorems without formally stating the hypotheses, relying on context to imply them.  E.g., the CPT theorem in field theory.  My understanding is that the equipartition result was referred to as the same theorem under various derivations from different hypotheses.  It may be an abuse of the language, but I think it's a common one.)  Gnixon 16:54, 2 May 2007 (UTC)

text: A move to "Equipartition" (dropping "theorem") sounds like a good idea.  If the article is about the theorem, I really think it needs to be stated in at least some form right up front (even in the lead instead of the first section).  Gnixon 16:54, 2 May 2007 (UTC)

text: ...although insisting on "form" for the element of surface area is a little excessive in this context.  ;-) Gnixon 18:26, 2 May 2007 (UTC)

text: Humor is clutch.  Once again, I think your edits have made a big improvement---no joke on that point.  I will try to fiddle with things once I get a reasonable block of time, but I think I could support now, too.  I never would have thought an article on equipartition could be so interesting.  Gnixon 22:34, 2 May 2007 (UTC)
thread_title:  Recent restructuring 

message: I'm happy for the two passing references to symplectic manifolds to be removed: the term "phase space" already covers this point, but I am not convinced it is any more friendly to our readers.
As for differential forms, the only occurence of this term is a casual remark I made in the edit history. In the text, the dot product is taken between a vector and an infinitesimal area without explaining what this means, so I added the word "form" to indicate that there might be something happening here! If anyone knows a better way to clarify this issue without entering into a large digression, please edit it! Geometry guy 22:15, 2 May 2007 (UTC)
replies: text: Regarding forms, since it's a concept that may be unfamiliar to readers otherwise comfortable with that section, I'd prefer referring to a normal vector---it's closer to the elementary treatment in multivariate calculus.  No need to wince if the application is simple enough that nobody will be confused!  On the other hand, it may be awkward to try and insert a description of the normal, so maybe we could get away with glossing over the issue by just calling it the element of surface area with no further explanation---some will know what is meant while those who don't probably won't notice any problems.  The "form" insertion is a nice way to handle it, too, but I'm worried that some student taking his first GR course will come along and insert a long parenthetical remark explaining what a form is in layman's terms---ugh.  I could go with any of three solutions---no explanation, normal vector, or form---depending on details of how it looks.  Gnixon 22:29, 2 May 2007 (UTC)
replies: text: Sorry, the word "form" leapt out at me in the ideal-gas-law derivation; being one of my own nightmares, I thought that others would be scared of it, too. ;)  But I'm flexible, too; I guess I would lean towards the finessed solution of "no explanation" to keep the focus, and just assume that Those who Know will know.  Hunting for refs, Willow 22:45, 2 May 2007 (UTC)

text: I find the math vastly more readable since you've gone through it.  My pledge to take a pass through things remains in effect, but it's been a busy week (sorry).  Gnixon 17:28, 3 May 2007 (UTC)
replies: text: Thank you very much, G-guy; the article reads much better with your touch!  I have to wonder at myself sometimes, but I'm very glad that someone here can think straight and lay out roads through labyrinths.  I'm a little embarrassed by the forms-thing, too, although I'm comforted by the fact that I'm not the only person in the world with math-phobia. ;) Usually I don't have to do anything harder than redesigning a dress for a different client or changing the gauge on a Fair Isle sweater pattern.  Both of those can be hard enough! :) Willow 19:09, 3 May 2007 (UTC)
thread_title: New math vs old

message: Congratulations to all involved on the FA. It seems are work is not all done, however: the following comments by User:Awadewit are copied over from my talk page (with permission).
:As a representative of the educated but not scientifically-trained masses (and an avid reader of popular science books), Willow asked me to look over the equipartition theorem article again for overly obscure language. As I wrote in my earlier peer review, I am not sure that this article is one that anyone will stumble on who doesn't have some mathematical and physical knowledge already (unlike, for example, natural selection), but I do believe that at least the lead of every article should make an attempt to be comprehensible by the non-specialist. I think that the lead for this article has improved, but, to me, the opening paragraph is overly specific (I am thinking here of for example, the average kinetic energy in the translational motion of a molecule should equal the average kinetic energy in its rotational motion). "Translation motion" and "rotational motion" may be obvious terms to physicists and mathematicians, but they were not to me (but perhaps that is just me). I would suggest that every attempt be made in the lead to explain equipartition in simple terms and leave the "meat" for the article. Unfortunately, I understood equipartition not from this article, but from my live-in physics expert who explained it to me after I read the article. There must be some way to convey the gist of equipartition to the non-specialist in this article - perhaps in a separate section? Awadewit Talk 20:04, 6 May 2007 (UTC)
thread_title:  Still work to be done! 

message: Third paragraph in the introduction "Equipartition's failure for electromagnetic radiation — also known as the ultraviolet catastrophe — led Albert Einstein to suggest that light itself was quantized into photons, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory." I believe it was Max Planck who suggested light was quantized not Einstein and it was not just due to the Ultraviolet catastrophe. See http://en.wikipedia.org/wiki/Ultraviolet_catastrophe —Preceding unsigned comment added by 65.32.59.88 (talk • contribs) 
:Thanks for writing! :)  You're right about multiple factors being involved in Einstein's hypothesis, first expressed in his 1905 paper.  However, Planck hypothesized that energy — or more strictly speaking, every change in energy involving electromagnetic radiation — was quantized, but not light.  He thought that the law ΔE = hν was not a property of light, but rather reflected some restriction on the nature of the things that emit light or on the emission process.  Planck opposed the quantization of light until roughly ten years after it was proposed, because he didn't want to have to change Maxwell's equations.  Hoping that this clarifies it rather than mudddles it — thanks again for your letter! :) Willow 11:25, 16 June 2007 (UTC)
thread_title: Equipartition and the rise of quantum theory

message: "The equipartition theorem can be used to derive the Brownian motion" it is impossible. Better "The equipartition theorem can be used to derive the mean square displacement of a Brownian particle" Alexander Mayorov (talk) 02:35, 20 October 2008 (UTC)
thread_title: Motion

message: The last sentence in the third paragraph of the introduction seems a bit clunky:
"Along with other evidence, equipartition's failure to model black-body radiation—also known as the ultraviolet catastrophe—led Max Planck to suggest that energy in the oscillators in an object, which emit light, were quantized, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory."
In particular, "energy" is the subject of the clause, and is singular. The verb "were" seems to disagree, as it is not singular.
I suggest this:
"...led Max Planck to suggest that the energy of the oscillators in objects that emit light is quantized, a revolutionary..."
It has fewer commas, and seems a bit smoother.  — Preceding unsigned comment added by 72.0.137.14 (talk) 14:31, 25 November 2011 (UTC)
thread_title:  A grammatical tweek... 

message: The images in this article are manually numbered in their captions (e.g. "Figure 2. Probability density...").  The trouble with the manual system is obvious: if one figure is moved or removed then the whole numbering system goes bad.  There's also the issue that some image numbers (e.g. the "Figure 1" in the header, which I just removed) go unreferenced in the article text, and serve only to clutter the caption.  Is there not an automatic figure numbering system for images akin to the existing Template:NumBlk for equations? TSchwenn (talk) 23:51, 17 April 2012 (UTC)
thread_title:  Numbering images/figures for reference 

message: In the intro it is suggested that max plank was trying to solve the ultraviolet catastrophe the page on this topic suggests otherwise hope this helps  — Preceding unsigned comment added by 114.77.88.235 (talk) 12:38, 2 September 2012 (UTC)
thread_title: max plank motivation

message: Such a collapse occurs ... when the gravitational potential energy exceeds twice the kinetic energy. I don't understand the factor of 2. Why is (3/2)NkT not enough? --egg 19:53, 4 September 2012 (UTC)
thread_title:  Star formation 

message: My recent revision has been reversed here
The I made the original change to emphasise that it is only kinetic energy that is exhanged in the equipartition theorem.
The equipartion theorem is a vital part of equilibrium thermodynamics, equipartition and thermal equilibrium (uniform temperature) meet the common requiremnt for uniform distribution of thermal energy, however there is absolutely no corresponding requirement for uniform distribution of potential energy - one only has to think of chemical energy to realise this. Similarly a triple point cell relies on the non-uniform distribution of potential energy for its temperature stability.
I would like comments on this before revising the article (again!). --Damorbel (talk) 17:32, 5 April 2013 (UTC)
thread_title:  Kinetic or Potential? 

message: I'm beginning a sort of WP:Expert review process for articles independent of the featured article system which I've realized has problems. As such, I've rated this article a level 'A' which means it is of the quality that would be expected from a professional reference work on the subject. I say this as a person with graduate degrees in astrophysics, but I encourage others who have similar qualifications to make comments if they believe my judgement to be incorrect.
jps (talk) 02:13, 12 September 2013 (UTC)
thread_title: WP:PHYSICS review: A-level article

message: Can anyone explain why in the general proof section, S=k_B \log \Sigma(E) instead of S=k_B \log \Gamma(E,\Delta E)?  — Preceding unsigned comment added by Zasdfgbnm (talk • contribs) 05:17, 6 February 2016 (UTC)
thread_title:  Entropy expression in general proofs section 

message: The article is tagged as "needing additional references from April 2015", "unsourced statements from March 2018", and "disputed statements from May 2018". The B-class criteria #1 states;  Reassess to C-class. 17:11, 1 March 2023‎ User:Otr500
:I believe that the article is actually reasonably well-sourced and the tags should have been removed some time ago. But a discussion about what needs sourcing, if anything, would be good to do. Qflib (talk) 20:36, 24 May 2024 (UTC)
thread_title: Article issues and classification