Axiomatics of Classical Statistical Mechanics, Volume 11

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

References

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

References

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

References

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

References

VI. Time-Independent Probability Distributions

20. Fluctuations in Statistical Equilibrium

21. Gibbs's Canonic Probability Distribution

References

VII. Statistical Thermodynamics

22. The Equation of State

23. The Fundamental Laws of Thermodynamics

24. Entropy and Probability

References

Index

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.