Mathematical Foundations of Statistical Mechanics

This book gives an excellant review of the theory behind statistical mechanics. This is a topic that is often left out of more popular books on statistical mechanics. It is a great companion to those other books.

This text will be of interests for people wanting to increase their knowledge in conceptual aspects of statistical mechanics. To read it ideally you should have a level of preparation comparable to Landau's book,but that's just ideally. In reality curious student interested in subject and having solid background in just basics of undergraduate level math being taught in physics departments could get most out of book. The book contains careful discussion of ergodic theory, topology of phase space and couple of important probabilistic theorems in a clear and elegant way. Name of the author is indicating that quality of book should be very high in terms of mathematical rigor and conceptual richness. Khinchin is one of the famous figures of last centuries brilliant mathematicians, who had contributed greatly to foundations of statistical mechanics and theory of stochastic processes. Despite the small size, this book requires some serious amount of mental work to fully grasp the content, so prepare your best pencil and clean papers and dive into mysterious world of statistical mechanics.

To read this book one needs some fundamental knowledge of mechanics and probability theory. The great author builds the foundations of statistical mechanics on these two pillars. Throughout the book the author develops the statistical theory of mechanics using an axiomatic approach and tries to invoke as few assumptions as possible. If you like the language of mathematics, this is the most elegant and concise book on classical equilibrium statistical mechanics. J.W.Gibbs's pioneering book, elementary principles of statistical mechanics, is not as readable as this one, in my opinion. In the appendix there is author's extension of the central limit theorem as a bonus!

A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. I can remember the vague feeling of dissatisfaction I felt as a student with some of the mathematics in Frederick Reif's "Fundamentals of Statistical and Thermal Physics" and other texts. Khinchin's little book puts everything on a firm mathematical foundation and yet is very readble.I liked all three of these books but I think I liked this one best. The English translation was done by the eminent physicist and writer George Gamow. Nicely typeset in modern notation with index. This book is also a real bargain.