Axiomatics of Classical Statistical Mechanics

Axiomatics of Classical Statistical Mechanics

1st Edition - January 1, 1960

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  • Editors: I. N. Sneddon, S. Ulam, M. Stark
  • eBook ISBN: 9781483194783

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Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.

Table of Contents

  • I. Introduction

    1. Statement of the Problem

    II. Mathematical Tools

    2. Sets

    3. Mapping

    4. Point Sets in the n-Dimensional Vector Space Rn

    5. Topological Mapping in Vector Spaces

    6. Systems of Ordinary Differential Equations

    7. The Lebesgue Measure

    8. The Lebesgue Integral

    9. Hubert Spaces


    III. The Phase Flows of Mechanical Systems

    10. Mechanical Systems

    11. Phase Flow; Liouville's Theorem

    12. Stationary Measure-Conserving Phase Flow; Poincaré's, Hopf's and Jacobi's Theorems

    13. The Theorems of V. Neumann and Birkhoff; The Ergodic Hypothesis


    IV. The Initial Distribution of Probability in the Phase Space

    14. A Formal Description of the Concept of Probability

    15. On the Application of the Concept of Probability


    V. Probability Distributions Which Depend on Time

    16. Mechanical Systems with General Equations of Motion

    17. Hamiltonian and Newtonian Systems

    18. The Initial Value Problem

    19. The Approach of Mechanical Systems Towards States of Statistical Equilibrium


    VI. Time-Independent Probability Distributions

    20. Fluctuations in Statistical Equilibrium

    21. Gibbs's Canonic Probability Distribution


    VII. Statistical Thermodynamics

    22. The Equation of State

    23. The Fundamental Laws of Thermodynamics

    24. Entropy and Probability



Product details

  • No. of pages: 190
  • Language: English
  • Copyright: © Pergamon 1960
  • Published: January 1, 1960
  • Imprint: Pergamon
  • eBook ISBN: 9781483194783

About the Editors

I. N. Sneddon

S. Ulam

M. Stark

About the Author

Rudolf Kurth

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