Foundations of Statistical Mechanics (eBook)

A Deductive Treatment

O. Penrose (Autor)

D. ter Haar (Herausgeber)

eBook Download: PDF

2016 | 1. Auflage
270 Seiten
Elsevier Science (Verlag)
9781483156484 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Foundations of Statistical Mechanics: A Deductive Treatment 4
Copyright Page 5
Table of Contents 6
Preface 8
The Main Postulates of this Theory 10
CHAPTER I. Basic Assumptions 12
1. Introduction 12
2. Dynamics 18
3. Observation 28
4. Probability 37
5. The Markovian postulate 43
6. Two alternative approaches 50
CHAPTER II. Probability Theory 56
1. Events 56
2. Random variables 61
3. Statistical independence 66
4. Markov chains 70
5. Classification of observational states 75
6. Statistical equilibrium 82
7. The approach to equilibrium 86
8. Periodic ergodic sets 92
9. The weak law of large numbers 97
CHAPTER III. The Gibbs Ensemble 105
1. Introduction 105
2. The phase-space density 107
3. The classical Liouville theorem 110
4. The density matrix 116
5. The quantum Liouville theorem 122
CHAPTER IV. Probabilities from Dynamics 127
1. Dynamical images of events 127
2. Observational equivalence 131
3. The classical accessibility postulate 134
4. The quantum accessibility postulates 138
5. The equilibrium ensemble 143
6. Coarse-grained ensembles 149
7. The consistency condition 155
8. Transient states 162
CHAPTER V. Boltzmann Entropy 166
1. Two fundamental properties of entropy 166
2. Composite systems 172
3. The additivity of entropy 178
4. Large systems and the connection with thermodynamics 184
5. Equilibrium fluctuations 191
6. Equilibrium fluctuations in a classical gas 197
7. The kinetic equation for a classical gas 204
8. Boltzmann's H theorem 210
CHAPTER VI. Statistical Entropy 219
1. The definition of statistical entropy 219
2. Additivity properties of statistical entropy 227
3. Perpetual motion 232
4. Entropy and information 237
5. Entropy changes in the observer 242
Solutions to Exercises 250
Index 260
OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY 272

Produkt-Details

• Erscheint lt. Verlag: 21.9.2016
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik
• ISBN-13: 9781483156484 / 9781483156484