Mathematical Foundations of Statistical Mechanics

Book Details

• Publisher: Dover

• Author: A.Y. Khinchin

• Language: English

• Edition: First Edition

• ISBN: 9780486601472

• Pages: 179

• Cover: Paperback

• Release Date: 01-06-1949

• Dimensions: 8.3 x 5.3 x 0.5 inches

About The Book
Mathematical Foundations of Statistical Mechanics by A.Y. Khinchin is a landmark text that offers a mathematically rigorous and clear introduction to the complex world of statistical mechanics. Aimed at English-speaking mathematicians and mathematical physicists, this translation brings an up-to-date and precise formulation of the problems encountered in statistical mechanics, distinguishing it from other works that often lack the necessary rigor.

In this comprehensive work, Khinchin replaces the cumbersome concepts typically used to establish basic formulae with analytical tools that provide clarity and depth. His approach gives a logical, step-by-step introduction that enables readers to quickly master the elements of statistical mechanics. The book begins with a historical overview and continues with a detailed discussion on the geometry and kinematics of phase space, incorporating the fundamental Liouville and Birkhoff theorems.

The book also covers critical topics such as the ergodic problem, in which time averages are replaced by phase averages, the theory of probability, and the central limit theorem. A significant portion of the text is dedicated to the ideal monatomic gas, the foundations of thermodynamics, and the dispersion and distribution of sum functions. With its rigorous treatment of the ergodic theorem (including a complete proof), as well as the lucid chapter on the statistical foundations of thermodynamics, this book is a valuable resource for both teachers and students.

Khinchin’s work has been praised for being clear, concise, and rigorous, making it indispensable for anyone seeking to understand statistical mechanics. Highly recommended by M. Kac in the Quarterly of Applied Mathematics, this text is perfect for those interested in gaining a deep and structured understanding of statistical mechanics.