Can anyone recommend a good book on Basic Statistical Mechanics? I have an engineering background and had to go through loads of different books to learn General Relativity. I found Peter Collier's A Most Incomprehensible Thing to be a fine book after Hartle's book on Gravity. So, is there any text which treats Statistical Mechanics in a simple, elementary enough way?
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I'd like to suggest Statistical Mechanics In a Nutshell - Luca Peliti. It presents deep knowledge in a very simple way. I like it mathematically also.
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In a introductory level, I think the best shot is Daniel V. Schroeder: An Introduction to Thermal Physics. It exposes thermodynamics in a modern point of view, connecting that to statistical mechanics. In other hand, the statistical mechanics is basic but solid in concepts. The best book I got in my undergraduation course. This book is easily find at libgen and there's a website with its content to read each section by time: https://physicspages.com/schroeder%20thermal.html.
There are a brazilian book considered so good, but I think it misses some important steps of physical and mathematical thoughts: Introdução à Física Estatística - S. Salinas. (Introduction to Statistical Physics - translated to english)
I've just found this one: Kurth R - Axiomatics of classical statistical mechanics (1960, Pergamon). I got your question while searching for references in Statiscal mechanics with mathematical perspective. This seems perfect to me, if you like math I suggest you this, after a first reading on Schroeder's book.
The more referenced authors in Statistical Mechanics are: Silvio Salinas (brazilian - undergraduate & graduate), Reif (undergraduate), Pathria (undergraduate & graduate), Greiner (graduate text)
The levels are exposed as usual.