Foundations of Statistical Mechanics

International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems of statistical mechanics. This book examines the theory that provides explicit recognition to the limitations on one's powers of observation.
Organized into six chapters, this volume begins with an overview of the main physical assumptions and their idealization in the form of postulates. This text then examines the consequences of these postulates that culminate in a derivation of the fundamental formula for calculating probabilities in terms of dynamic quantities. Other chapters provide a careful analysis of the significant notion of entropy, which shows the links between thermodynamics and statistical mechanics and also between communication theory and statistical mechanics. The final chapter deals with the thermodynamic concept of entropy.
This book is intended to be suitable for students of theoretical physics. Probability theorists, statisticians, and philosophers will also find this book useful.

Contenu

Preface
The Main Postulates of this Theory
Chapter I Basic Assumptions

1. Introduction
2. Dynamics
   2.1. Exercises
3. Observation
   3.1. Exercises
4. Probability
5. The Markovian Postulate
   5.1. Exercises
6. Two Alternative Approaches
   Chapter II Probability Theory
7. Events
   1.1. Exercises
8. Random Variables
   2.1. Exercise
9. Statistical Independence
   3.1. Exercises
10. Markov Chains
    4.1. Exercises
11. Classification of Observational States
    5.1. Exercises
12. Statistical Equilibrium
    6.1. Exercises
13. The Approach to Equilibrium
    7.1. Exercises
14. Periodic Ergodic Sets
    8.1. Exercises
15. The Weak Law of Large Numbers
    9.1. Exercises
    Chapter III The Gibbs Ensemble
16. Introduction
17. The Phase-Space Density
    2.1. Exercise
18. The Classical Liouville Theorem
    3.1. Exercises
19. The Density Matrix
    4.1. Exercises
20. The Quantum Liouville Theorem
    5.1. Exercises
    Chapter IV Probabilities from Dynamics
21. Dynamical Images of Events
    1.1. Exercise
22. Observational Equivalence
    2.1. Exercise
23. The Classical Accessibility Postulate
    3.1. Exercises
24. The Quantum Accessibility Postulates
    4.1. Exercises
25. The Equilibrium Ensemble
    5.1. Exercises
26. Coarse-Grained Ensembles
    6.1. Exercises
27. The Consistency Condition
    7.1. Exercises
28. Transient States
    8.1. Exercise
    Chapter V Boltzmann Entropy
29. Two Fundamental Properties of Entropy
30. Composite Systems
    2.1. Exercise
31. The Additivity of Entropy
    3.1. Exercises
32. Large Systems and the Connection with Thermodynamics
    4.1. Exercises
33. Equilibrium Fluctuations
    5.1. Exercises
34. Equilibrium Fluctuations in a Classical Gas
    6.1. Exercises
35. The Kinetic Equation for a Classical Gas
36. Boltzmann's H Theorem
    8.1. Exercise
    Chapter VI Statistical Entropy
37. The Definition of Statistical Entropy
    1.1. Exercises
38. Additivity Properties of Statistical Entropy
    2.1. Exercises
39. Perpetual Motion
    3.1. Exercise
40. Entropy and Information
41. Entropy Changes in the Observer
    5.1. Exercises
    Solutions to Exercises
    Index
    Other Titles in the Series