Talk:Statistical mechanics/Comments

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The discussion of 'fundamental postulate' is incorrect. It refers only to the formulation of Boltzmann, and not to the very different formulation of Josiah Willard Gibbs. In understanding the difference between the Gibbs and Boltzmann approaches, you actually have to read Gibbs' book Elementary Principles in Statistical Mechanics, and not later summaries, most of which appear to pass through Paul and Tatiana Ehrenfest's 1912 article "The Conceptual Foundations of the Statistical Approach in Mechanics", now available from Dover Press as a mostly-English translation. I am reasonably sure that I am not the first to have noted that the Ehrenfest presentation of Gibbs' book does not do as well as might have been desired by Gibbs, but that needs to be researched.

A few issues are treated in my textbook "Elementary Lectures in Statistical Mechanics, Springer-Verlag). In particular, in the actual book by Gibbs, which is reasonably a reliable source on what Gibbs wrote:

1) Gibbs used a different fundamental postulate, _not_ the principle of equal a priori probabilities, because Gibbs viewed the canonical ensemble as primary and the microcanonical ensemble as secondary. In modern notation, Gibbs viewed W_j = exp(- beta E_j) as fundamental.

2) The notion that statistical mechanics is only applicable to large systems is not found in Gibbs' book. Indeed, he deliberately compares his treatment with a treatment that he does not identify as Boltzmann's, showing the differences in the predictions of teh two models.

3) Gibbs certainly does not speak of the H-Theorem. After all, in Gibbsian statistical mecahnics the entropy is a constant of the motion.