Talk:Canonical ensemble

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The canonical partition function is introduced at the beginning of article. IMHO, this concise result itself is more important than its derivations. Czhangrice 05:33, 25 May 2007 (UTC)


Contents

[edit] creating a new section of comparison with other ensembles

Yes, yes, I know... :-) --HappyCamper 21:56, 6 January 2006 (UTC)
What about removing the referrals to other ensembles in the introduction. Even for someone who knows what a canonical ensemble is, this is just too confusing. -- Mipmip 12:33, 13 November 2006 (UTC)
IMHO, the comparisons should be kept. you wanna give it a go at improving the readability of that passage, from your perspective? then we'll see what other folks think. Mct mht 11:00, 1 December 2006 (UTC)
I agree. The connection with other ensembles are not very essential in understanding the canonical ensemble itself. I create a separate section for these contents. Czhangrice 05:33, 25 May 2007 (UTC)


[edit] about the ensemble derivation

One point I tried to make clear is that the heat bath is not necessary in the ensemble theory, other systems in the ensemble naturally serve as an effective heat bath. Since we are talking about the canonical ensemble, probably it is better to write the article from the ensemble viewpoint. However, I am aware that the heat-bath way of introducing canonical ensemble is a common introducing derivation, and it is widely used in textbooks. Anyway, this is only my personal preference. Czhangrice 05:33, 25 May 2007 (UTC)



[edit] redirect suggestion

Suggested redirect from "Gibbs ensemble"

[edit] primary content critique

As a discussion of J. W. Gibbs' canonical ensemble, and Gibbs did create the ensemble approach in his 1902 book, the bulk of the discussion here is wrong. What you have here is a discussion of how someone using the Boltzmann treatment of statistical mechnics would reach a canonical ensemble.

Gibbs axiomatization of statistical mechanics is completely different. The formulation found in Gibbs book does have states of the ensemble, but they are entirely noninteracting, and do not form a bath. Gibbs did not invoke or accept the so-called 'principle of equal a priori probabilities' as being fundamental. Indeed, he goes on at great length (for Gibbs) to show why the equal a priori probabilities approach and the microcanonical ensemble is inferior to his approach. Perhaps someone has time to read his book (as I did while writing my book Elementary lectures in Statistical Mechanics) and get this right, but I am too busy these days.

the derivation seems fine. IIRC, at least one graduate stat mech text gives a presentation along this line. if the point is that the microcanonical ensemble equal-probability assumption is not needed, it's not used in the article. the sentence in the introducion is meant to indicate an alternative derivation. the fact that the system is coupled to a reservoir is same as saying it's in equilibrium, which is reasonable. and indeed one can define a Gibbs ensemble to be the probability measure induced by the Gibbs distribution. this is hinted at in the article quantum statistical mechanics, and is standard in mathematical literature. in fact, i've never seen it defined otherwise there. Mct mht 10:57, 19 November 2006 (UTC)
see also the section re the QM Gibbs state of article. Mct mht 11:02, 19 November 2006 (UTC)
also, i believe the microcanonical-ensemble derivation of the Gibbs ensemble, which does not appear in the article, is by now pretty standard, regardless of what Gibbs believed. to claim that it's wrong would not be right. Mct mht 11:12, 19 November 2006 (UTC)
BTW, i'd interested in a second opinion. i have not read Gibbs original book. but it seems that the a priori equal probability postulate (therefore the microcanonical ensemble):
The equilibrium distribution of the macroscopic states of an isolated system is the uniform distribution on the energy surface.
is fundamental to much of statistical mechanics and commonly attributed to Gibbs. this may be an indication that the critique above is a misinterpretation. or, at least, the difference claimed is only a historic one and makes no basic difference in the development and understanding of the subject. Mct mht 06:41, 25 November 2006 (UTC)

[edit] helmholtz energy or free energy

An anonymous user recently edited the page to be in accordance with [http://www.iupac.org/goldbook/H02772.pdf], where it is written that currently it should not be called "free energy" but "helmholtz energy". I don't like the looks of this, but it's still a IUPAC standard. Shouldn't we comply? Current state is "helmholtz free energy" and I am very happy with that myself, I'm just being advocate of the devil here :) -- Mipmip 21:21, 3 January 2007 (UTC)

Every reference I've seen uses "Helmholtz Free Energy". Simply 'free energy' is not specific enough, and Helmholtz Energy, while better, has the potential for being confused with something else. Helmholtz Free Energy is a subset of the general concept of Free Energy, so that's the term I'd prefer.Sojourner001 16:44, 17 January 2007 (UTC)
D'oh. I've just read the discussion you posted. Further to this, let me change my opinion.
Redirect Helmholtz Free Energy to Helmholtz Energy as per IUPAC, and add a note at the very top to explain the disparity. It's important to both be correct and accomodate the habits of those in the know.Sojourner001 16:56, 17 January 2007 (UTC)
The canonical place to discuss this question would appear to be Talk:Gibbs free energy. The outcome of an extensive discussion in 2006, with many viewpoints raised, which can be read at Talk:Gibbs free energy/Archive1, was strong consensus for No change -- ie to keep the article titles as Gibbs free energy and Helmholtz free energy.
I have to say that I too would support this. There are many different "named" energies in Physics. It is useful to distinguish these two by calling them free energies. Jheald 11:15, 6 March 2007 (UTC)