Mathematical Foundations of Statistical Mechanics

by Aleksandr Yakovlevich Khinchin, George Gamow (Translator)

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions.

Genres: Physics, Mathematics, Science

206 pages, Paperback

First published December 12, 1949

About the author

Алекса́ндр Я́ковлевич Хи́нчин
A.I. Khinchin
A.Y. Khinchin
A. Ya. Khinchin

Reviews

[Ross · Rating 3 out of 5]

The age and mathematical rigor (not to mention the fact that it is translated) all add to the difficulty of this text. However, with some effort, one can gain a great deal of insight into the mathematics behind statistical mechanics. The book is filled with proofs and theorems and is a great resource for mathematicians. For a physicist, however important these foundations are, the connexions between the proofs and the end result, the applications to the real world, are a bit labored throughout most of the book. Still probably worth having on your bookshelf.

[Christian Kotz · Rating 4 out of 5]

Tough read, but good book.

[William Schram · Rating 5 out of 5]

This book is quite challenging, mostly because I don't know mathematics. If I knew more about grad and Lebesgue, I suppose it would come out better. As I stand, I can't understand this book all that well, and I need to have a stepping stone for it. Sometimes being an autodidact is tough. No classes or anything really make things complicated.

On the other hand, the book is written pretty well; it's mostly equations and text. Not a lot of pictures, it somewhat explains the units and symbols used, but I don't have the background for it. Perhaps if I revisit some Calculus and linear algebra, I can then come back to this book again.

Edit: Ten years later, and I understand the material far more easily. I am still learning the subject for fun, so if I took classes or had some more structure, I could probably do better.

The book is clearly written. Aleksandr Yakovlevich Khinchin intended the material for a mathematician learning the subject. George Gamow also did a great job with the translation.

There are no practice problems to solve in the book.