## Mathematical Foundations of Statistical MechanicsThe translation of this important book brings to the English-speaking mathematician and mathematical physicist a thoroughly up-to-date introduction to statistical mechanics. It offers a precise and mathematically rigorous formulation of the problems of statistical mechanics, as opposed to the non-rigorous discussion presented in most other works. It provides analytical tools needed to replace many of the cumbersome concepts and devices commonly used for establishing basic formulae, and it furnishes the mathematician with a logical step-by-step introduction, which will enable him to master the elements of statistical mechanics in the shortest possible time. After a historical sketch, the author discusses the geometry and kinematics of the phase space, with the theorems of Liouville and Birkhoff; the ergodic problem (in the sense of replacing time averages by phase averages); the theory of probability; central limit theorem; ideal monatomic gas; foundation of thermodynamics, and dispersion and distribution of sum functions. "An excellent introduction to the difficult and important discipline of Statistical Mechanics. It is clear, concise, and rigorous. There is a very good chapter on the ergodic theorem (with a complete proof!) and . . . a highly lucid chapter on statistical foundations of thermodynamics . . . useful to teachers . . . and to mathematicians." ? M. Kac, Quarterly of Applied Mathematics. |

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### Contents

Geometry and Kinematics of the Phase Space | 13 |

Ergodic Problem | 44 |

Reduction to the Problem of the Theory | 70 |

Application of the Central Limit Theorem | 84 |

Ideal Monatomic | 115 |

The Foundation of Thermodynamics | 129 |

Dispersion and the Distributions of | 148 |

Appendix | 162 |

Notations | 176 |

### Other editions - View all

Mathematical Foundations of Statistical Mechanics Aleksandr I?Akovlevich Khinchin Limited preview - 1949 |

### Common terms and phrases

according ANALYSIS applications approximate argument assume asymptotic calculation chapter classical clear completely component condition consider considerations consists constant energy contained corresponding definition denote density depend derived determined DIFFERENTIAL distribution law dynamic coordinates entire entropy equal equations ergodic estimate example exists expression external fact follows forces formula fundamental given system gives hand ideal important integral interval introduction large number limit mathematical mean value measure method metric molecule motion natural normal obtain parameters particles particular phase averages phase function phase space physical positive possible present problems proof properties prove quantity quantum quantum mechanics random relation remains represents segment selected sense statistical mechanics structure function sufficiently surface surface of constant system G theorem theory of probability thermodynamics tion trajectory usually variables volume write