Foundations of Classical and Quantum Statistical Mechanics

Foundations of Classical and Quantum Statistical Mechanics

International Series of Monographs in Natural Philosophy

1st Edition - January 1, 1963

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  • Author: R. Jancel
  • eBook ISBN: 9781483186269

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Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.

Table of Contents

  • Preface

    Preface to the English Edition

    General Introduction

    Part I. Ergodic Theory

    Chapter I. The Ergodic Theory in Classical Statistical Mechanics

    I. Statistical Ensembles of Classical Systems

    II. Ergodic Theorems in Classical Mechanics

    III. The Hypothesis of Metric Transitivity

    Chapter Ii. Quantum Mechanical Ensembles. Macroscopic Operators

    I . Statistical Ensembles of Quantum Systems

    II. Macroscopic Operators

    Chapter III. The Ergodic Theorem in Quantum Statistical Mechanics

    I. The Ergodic Problem in Quantum Mechanics

    II. The First Quantum Ergodic Theorem

    III. The Second Quantum Ergodic Theorem

    IV. The Proofs of Von Neumann and Pauli-Fierz

    Chapter IV. Probability Quantum Ergodic Theorems

    I. Comments on the Quantum Ergodic Theory

    II. First Probability Ergodic Theorem

    III. The Macroscopic Probability Ergodic Theorem

    IV. Statistical Properties of Macroscopic Observables. Comparison with Classical Theory

    V. Relations between Microcanonical, Canonical and Grand-Canonical Ensemble

    Part II. H-Theorems


    Chapter V. H-Theorems and Kinetic Equations in Classical Statistical Mechanics

    I. Mechanical Reversibility and Quasi-Periodicity

    II. Coarse-Grained Densities and the Generalized H-Theorem

    III. Transition Probabilities and Boltzmann's Equation

    IV. Stochastic Processes and H-Theorems

    V. Integration of the Liouville Equation

    VI. Prigogine's Theory of Irreversible Processes

    Chapter VI. H-Theorems and Kinetic Equations in Quantum Statistical Mechanics

    I. Fine- and Coarse-Grained Densities in Quantum Mechanics

    II. The H-Theorem for an Ensemble of Quantum Systems

    III. The Kinetic Equation and Irreversible Processes

    IV. Boltzmann's Equation and Stochastic Processes in Quantum Theory

    V. Zwanzig's Method

    Chapter Vii. General Conclusions. Macroscopic Observation and Quantum Measurement

    I. Applications of Statistical Mechanics

    II. Quantum Measurement and Macroscopic Observation

    Appendix I

    1. Historical Review of Ergodic Theory

    2. Birkhoff's Theorem

    3. Notes On the Metric Transitivity of Hypersurfaces

    4. Structure Functions in Classical Statistical Mechanics

    Appendix II. Probability Laws in Real n-Dimensional Euclidean Space

    1. The Unit Hypersphere in n-Dimensional Space

    2. The Unit Hypersphere in 2n-Dimensional Space 340

    3. Probability Laws for the Quantities Dii(y) and µij(α)

    Appendix III A. Ehrenfests' Model

    1. The Function H(Z, t) and the "H-Curve"

    2. Ehrenfests' Model

    3. Transition Probabilities and the Fundamental Equation

    4. Stationary Distribution

    5. Properties of the "Δs-Curve"

    6. Calculation of P(n│m, s)

    Appendix III B. Notes on the Definition of Entropy

    Appendix IV. Note on Recent Developments in Classical Ergodic Theory

    I. The Concept of an Abstract Dynamic System

    II. Asymptotic Properties of Abstract Dynamic Systems

    1. Definitions

    2. Asymptotic Properties

    III. Entropy and K-Systems

    1. Measurable Decompositions

    2. Entropy

    3. K-Systems



Product details

  • No. of pages: 440
  • Language: English
  • Copyright: © Pergamon 1963
  • Published: January 1, 1963
  • Imprint: Pergamon
  • eBook ISBN: 9781483186269

About the Author

R. Jancel

About the Editor

D. ter Haar

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