Axiomatics of Classical Statistical Mechanics
- 1st Edition, Volume 11 - September 20, 2014
- Latest edition
- Author: Rudolf Kurth
- Editors: I. N. Sneddon, S. Ulam, M. Stark
- Language: English
Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a… Read more
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.
I. Introduction 1. Statement of the ProblemII. 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 ReferencesIII. 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 ReferencesIV. 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 ReferencesV. 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 ReferencesVI. Time-Independent Probability Distributions 20. Fluctuations in Statistical Equilibrium 21. Gibbs's Canonic Probability Distribution ReferencesVII. Statistical Thermodynamics 22. The Equation of State 23. The Fundamental Laws of Thermodynamics 24. Entropy and Probability ReferencesIndex
- Edition: 1
- Latest edition
- Volume: 11
- Published: September 20, 2014
- Language: English
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