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Mathematical Foundations of Statistical Mechanics

by A. Khinchin

A mathematical route into statistical mechanics

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AlbakiReads Editorial

A mathematical route into statistical mechanics

This 2014 facsimile reprint of the 1949 edition presents statistical mechanics through mathematical formulation and analysis. Its contents move from phase-space geometry and kinematics to the ergodic problem, probability theory, and the central limit theorem, then apply these ideas to an ideal monatomic gas and the foundations of thermodynamics. The closing material addresses dispersion and distributions of sum functions. The stated emphasis is on a logical, step-by-step introduction in mathematical terms, making the book’s scope especially clear: it connects probability methods with core problems in statistical mechanics. The source identifies A. Khinchin as a mathematician associated with the Soviet school of probability theory.

Good fit for readers who enjoy

  • Mathematicians and physicists approaching statistical mechanics for the first time
  • Readers interested in probability-theoretic foundations of mechanics and thermodynamics

Themes

Statistical mechanicsProbability theoryPhase space and ergodic problemsThermodynamics

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Book overview

2014 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The translation of this important work brings to the American mathematician and physicist a useful work of statistical mechanics. It offers a precise and mathematically satisfactory formulation of the problems of statistical mechanics and provides the analytic tools needed to replace many of the cumbersome concepts and devices commonly found in more basic works on the subject. And above all, it furnishes the mathematician approaching the subject for the first time with a logical, step-by-step introduction, written in mathematical terms, to aid in mastering the subject in the shortest possible time. Contents Include: Geometry and kinematics of the phase space. -- Ergodic problem. -- Reduction to the problem of the theory of probability. -- Application of the central limit theorem. -- Ideal monatomic gas. -- The foundation of thermodynamics. -- Dispersion and the distributions of sum functions. Aleksandr Khinchin was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory.
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