
Axiomatics of Classical Statistical Mechanics
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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
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
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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