Foundations of Statistical Mechanics
A Deductive Treatment
- 1st Edition - October 30, 2013
- Latest edition
- Author: O. Penrose
- Editor: D. Ter Haar
- Language: English
International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems… Read more
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.
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
1. Events
1.1. Exercises
2. Random Variables
2.1. Exercise
3. Statistical Independence
3.1. Exercises
4. Markov Chains
4.1. Exercises
5. Classification of Observational States
5.1. Exercises
6. Statistical Equilibrium
6.1. Exercises
7. The Approach to Equilibrium
7.1. Exercises
8. Periodic Ergodic Sets
8.1. Exercises
9. The Weak Law of Large Numbers
9.1. Exercises
Chapter III The Gibbs Ensemble
1. Introduction
2. The Phase-Space Density
2.1. Exercise
3. The Classical Liouville Theorem
3.1. Exercises
4. The Density Matrix
4.1. Exercises
5. The Quantum Liouville Theorem
5.1. Exercises
Chapter IV Probabilities from Dynamics
1. Dynamical Images of Events
1.1. Exercise
2. Observational Equivalence
2.1. Exercise
3. The Classical Accessibility Postulate
3.1. Exercises
4. The Quantum Accessibility Postulates
4.1. Exercises
5. The Equilibrium Ensemble
5.1. Exercises
6. Coarse-Grained Ensembles
6.1. Exercises
7. The Consistency Condition
7.1. Exercises
8. Transient States
8.1. Exercise
Chapter V Boltzmann Entropy
1. Two Fundamental Properties of Entropy
2. Composite Systems
2.1. Exercise
3. The Additivity of Entropy
3.1. Exercises
4. Large Systems and the Connection with Thermodynamics
4.1. Exercises
5. Equilibrium Fluctuations
5.1. Exercises
6. Equilibrium Fluctuations in a Classical Gas
6.1. Exercises
7. The Kinetic Equation for a Classical Gas
8. Boltzmann's H Theorem
8.1. Exercise
Chapter VI Statistical Entropy
1. The Definition of Statistical Entropy
1.1. Exercises
2. Additivity Properties of Statistical Entropy
2.1. Exercises
3. Perpetual Motion
3.1. Exercise
4. Entropy and Information
5. Entropy Changes in the Observer
5.1. Exercises
Solutions to Exercises
Index
Other Titles in the Series
- Edition: 1
- Latest edition
- Published: October 30, 2013
- Language: English
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