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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)
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)
Suggested redirect from "Gibbs ensemble"
The canonical ensemble and Gibbs ensemble are DIFFERENT things. Gibbs canonical ensemble should NOT redirect to canonical ensemble, but to Isothermal–isobaric ensemble. —Preceding unsigned comment added by 76.23.5.194 ( talk) 02:57, 1 April 2011 (UTC)
No, this is not correct. Gibbs ensemble should not redirect to either. It should direct the reader to a new page that discusses the Gibbs ensemble Monte Carlo method developed by A. Z. Panagiotopoulos. — Preceding
unsigned comment added by
141.217.11.17 (
talk)
22:13, 2 September 2012 (UTC)
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.
An anonymous user recently edited the page to be in accordance with [ http://goldbook.iupac.org/goldbook/H02772.html], 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)
there seems to be something wrong with this section. in the expression for W({n_i}), i is used as an indexing variable so the argument n_i doesn't enter into the expression. maybe it's just confusing notation; i don't know enough about the subject to fix it.
I merged Canonical probability distribution into this article. The change to this article is minimal (a link and a date) since that article was just a stub. I am mentioning it here is on the off-chance that they don't deserve to be merged. TStein ( talk) 22:08, 8 May 2009 (UTC)
This article contains a very confusing statement that needs to be revised ASAP.
"The canonical ensemble is also called the Gibbs ensemble, in honor of J.W. Gibbs"
This may be true on some level, although technically the canonical ensemble is simply one of multiple ensembles derived by Gibbs. The real problem occurs when the uninitiated read this and confuse Monte Carlo simulations in the canonical ensemble with the Gibbs ensemble Monte Carlo technique and think they are the same thing. They are most definitely not!
Maybe you could consider that an explanation for the irreversibility of macroscopic process could be in the irreversibility of the measurement process in quantum mechanics (the collapse of the wavefunction). In Statistical Mechanics of Landau is demonstrated that entropy vs. time is a monotone function, the only thing that is not demonstrated is if the function is increasing or decreasing
Raúl Aparicio Bustillo-- 87.221.209.63 ( talk) 05:39, August 11, 2012
I would like to see a solid reference for this section because the writer claims extraordinary claims that are not accepted by the general scientific community. Specifically claims like:
The experimental data show that quantum-mechanical probability does not cover the entire probabilistic nature of the microworld and that God plays dice not exactly the way prescribed by Schrödinger. It forces us to reflect that the possibility of using the canonical distribution can be connected with internal processes in macrosystems, not described by the existing formalism of quantum mechanics.
The only reference i see regarding this section is a reference to a new non journal accepted article : "V.A. Skrebnev, Canonical distribution and incompleteness of quantum mechanics, arXiv:1201.5078v1 [physics.gen-ph]". This is nonsense and i demand that this entire section be removed until the author can back his claims with legitimate sources.
(Dean Mark 19:32, 7 November 2012 (UTC)) — Preceding unsigned comment added by DeanMrk ( talk • contribs)
Yes, this is a common derivation method... the article is presented in exactly the same step-by-step manner as you would find in MOST statistical mechanics (especially from the perspective of physical/theoretical chemistry) books.
But, possibly in an attempt to keep it succinct, the section reads like a reminder for someone who forgot their stat mech. Understanding the insight into WHY each step is chosen is important, not just physically but also mathematically. Why do assume what we assume? How did we come to this conclusion? Someone who is familiar with some of the mathematics might not immediately see why we would NEED to use Stirling's Approximation.... because we are dealing with factorials of very large numbers, and through the behavior of the logarithm we can simplify it and even approximate it. It might even be good to suggest the relationships between thermodynamic beta, the temperature, the configurational entropy, and the microcanonical ensemble.
184.189.220.114 (
talk)
09:17, 23 November 2012 (UTC)
I return to F designation as A occupied by the surface. This creates problems, for the canonical ensemble, which partition function contains the surface, but also connected with a free energy. Luksaz ( talk) 19:45, 15 February 2015 (UTC)