Wikipedia:Scientific peer review/Equipartition theorem

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[edit] Equipartition theorem

Hi, this is a pretty important classical physics topic. Its failures helped to spawn quantum mechanics and even now it's pretty useful. Please let me know what you all think of the presentation, and derivations. I'll try to flesh out the article titles and page numbers for the 19th century journal references but, if you happen to know of some already, I'd be very grateful. I'd like to bring this to Featured Article status in the near future. Thanks for your time and thoughtful reviews, Willow 20:08, 29 March 2007 (UTC)

[edit] Cryptic C62

I'll read through it and comment as I go.

• "Similar examples could be cited for every ..." this sentence is very unencyclopedic and unnecessary. Fixed
• What are "first principles" ? Fixed
• Can theorems form alliances? "The history of the equipartition theorem is closely allied with that of specific heats" Fixed
• There are alot of "unknowns" and question marks in the references. I'll work on this; it's hard to track down 19th-century references! :(
• You have a lot of high-quality sources. However, these all seem to be used in the History section. Make sure the applications and equations are well-referenced. The entire Derivations section is missing citations. Fixed
• "Pair potential" is red-linked. Either whip up an article for it or give a brief explanation here, as it's not a well-known concept. Fixed
• I doubt this is even possible, but if you can find or create a visual for this article, it would definitely help. It is very dense reading, as would be expected of physics theorems.

On the positive side, this information seems very comprehensive and well-organized. Keep at it! --Cryptic C62 · Talk 03:31, 31 March 2007 (UTC)

Thank you very much, Cryptic! :) I'll try to address your concerns. Willow 16:16, 2 April 2007 (UTC)

[edit] Jheald

A couple of comments, not a full review (more comprehensive comments, maybe, in a day or two)

• Something the article does is link to Hamiltonian quite early on with relatively little explanation. Despite my first instincts, I quite like that the article does this, because it's a useful set-up for the relativistic gas example, which is a very useful corrective to the idea that the energy is always ½kT per degree of freedom. But the idea of a Hamiltonian is quite an advanced concept compared to the entry level for a lot of the potential audience for this article. And Wikipedia isn't giving you much help at the moment. At the moment the link of the page is pointing to the Hamiltonian disambig page - which probably isn't going to help, if a reader has never heard of the word before. But the articles WP does currently have, eg Hamiltonian system, Hamiltonian mechanics, Hamilton's principle and Hamilton's equations don't currently altogether help either -- I fear that none of them has an introduction/summary which is pitched remotely simply enough for the entry-level of people coming to this article; and they could use being knocked together big-time. The one which probably most ought to be fixed up as a potential entry-point is Hamiltonian mechanics, which is supposed to be the category lead for Category:Hamiltonian mechanics. An introductory paragraph there, after the contents, glossing (but not proving) some of the results set out in Hamilton's equations, in particular H=T+V and the form of the equations of motion, might be the way to go. In fact the best solution would probably be to merge the two pages together outright, with most of the content now at Hamilton's equations coming in first, and the material now at Hamiltonian mechanics coming in as things get more sophisticated.

You're definitely right, although I had hoped to avoid all the work. When I first started out here, I also encountered some difficulties with a few pure-math Wikipedians over my overly basic description of the Hamilton-Jacobi equation; I kind of dread having to wrangle with them again. :(

Okay, I've added the merge tags, as an indicative first step. Let's see whether anybody wails! Jheald 14:14, 3 April 2007 (UTC)

• Pictures. It might be nice to show a pic of something like the Maxwellian distribution of 1d kinetic energies, with 1/2 kT marked, to show how much energy spread there can be in a single quadratic co-ordinate; and then a pic of the energy per d.o.f. for 3d and say 12d, to show how the energy per d.o.f. becomes very sharply defined for systems of more degrees of freedom as the Central Limit Theorem kicks in. Would pics for the corresponding relativistic gas show nice qualitative differences ?
• Pics showing the effects of frozen-out d.o.f.s due to energy-level spacing might be nice, too - showing how this makes an impact even before you put in Bose-Einstein or Fermi-Dirac effects. The nice thing about pics is they allow you to talk qualitatively about the effects, while being able to defer the quantitative details.

Maybe there's a way of combining these two figures to show how equipartition fails when you go from continuous to quantized energy levels. I'll brood on it for a few days.

• For the very simple quadratic case, would it be an idea to work through the maths starting with Boltzmann factors from the canonical distribution? Without prejudice to the more detailed and general derivations still being considered later.

Just some thoughts. Jheald 20:18, 2 April 2007 (UTC)

Yes, maybe. I'll try to add that and let's see how it flies! :) Thanks for your comments! Willow 11:55, 3 April 2007 (UTC)