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I saw Book recommendations
No reference to Statistical Mechanics there.

I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math.
And of course it's always good to give as much intuition about the material.

Some things I'd be happy if it includes (but again it mostly just needs to be a good clear book even if it doesn't contain these) are:

  1. As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates

  2. Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas.

Thank you

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A good advanced book that covers in details and with mathematical rigor what you want and much more is Gallavotti's "Statistical Mechanics - a short treatise", which is not so short actually... You can get it from here. –  Yvan Velenik Jun 21 '12 at 20:07
    
Another good (but probably too advanced) book is the "old" book by Ruelle, "Statistical Mechanics - Rigorous Results". If you have the level in maths, and are interested in the mathematical theory of phase transitions for lattice systems, the classical reference is Georgii's "Gibbs measures and phase transitions" (although that's more graduate level stuff). –  Yvan Velenik Jun 21 '12 at 20:09
    
Just in case. Here are the google book pages for the last 2 refs, so that you can have an idea of what is done there and at which level: Ruelle, Georgii. –  Yvan Velenik Jun 22 '12 at 16:15
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5 Answers

EDIT: My answer assumes that you're looking for a book at the introductory graduate level.

I found Pathria's "Statistical Mechanics" (2nd ed) very helpful during my first-year graduate statistical mechanics course. Pathria's treatment of the subject is mathematically careful and detailed, at least by physics standards; I found his discussion of Liouville's theorem (part 1 of your question) satisfactory. Unfortunately, like many formal treatments, Pathria discusses few interesting applications.

"Statistical Physics of Particles" by Kardar appears to be supplanting Pathria as the favored introductory graduate text; it was used at Boston University and at Caltech during my time there. Kardar is very terse and would probably have to be supplemented by another book, but the problems he offers are interesting (if hard). In fact, about a third of the text consists of detailed solutions to the problems.

I have heard good things about Reichl's book, already mentioned in another answer. I used it briefly as a reference: the coverage of kinetic theory is more complete than in other sources. It is more accessible than Pathria, not to mention Kardar.

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I recommend the book ''A Modern Course in Statistical Physics'' by Reichl. It starts with phenomenological thermodynamics, covers both equilibrium and nonequilibrium statistical mechanics, and discusses a wide range of applications, not only ideal and real gases. Its level of rigor is that of typical books on theoretical physics.

You may also be interested in my book http://lanl.arxiv.org/pdf/0810.1019v2.pdf ; the part on statistical mechanics is nearly independent of the remainder.

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I recommend books by Kardar "Statistical Physics of Particles" "Statistical Physics of Fields" The mordern approach to this subject is helpful for your future study.

Also there are solutions to all of the problem, which you can find from the internet.

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If anyone is interested in seeing how this is done from a chemist's perspective I can heartily recommend Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman. Sadly, it isn't on line but can be ordered from Amazon or the like.

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As an undergrad, we used "Thermal Physics" by Kittel and Kroemer:

http://www.amazon.com/Thermal-Physics-Edition-Charles-Kittel/dp/0716710889

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