E-Book, Englisch, 270 Seiten, Web PDF
Penrose / Ter Haar Foundations of Statistical Mechanics
1. Auflage 2016
ISBN: 978-1-4831-5648-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
A Deductive Treatment
E-Book, Englisch, 270 Seiten, Web PDF
ISBN: 978-1-4831-5648-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
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Weitere Infos & Material
1;Front Cover;1
2;Foundations of Statistical Mechanics: A Deductive Treatment;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;The Main Postulates of this Theory;10
7;CHAPTER I. Basic Assumptions;12
7.1;1. Introduction;12
7.2;2. Dynamics;18
7.3;3. Observation;28
7.4;4. Probability;37
7.5;5. The Markovian postulate;43
7.6;6. Two alternative approaches;50
8;CHAPTER II. Probability Theory;56
8.1;1. Events;56
8.2;2. Random variables;61
8.3;3. Statistical independence;66
8.4;4. Markov chains;70
8.5;5. Classification of observational states;75
8.6;6. Statistical equilibrium;82
8.7;7. The approach to equilibrium;86
8.8;8. Periodic ergodic sets;92
8.9;9. The weak law of large numbers;97
9;CHAPTER III. The Gibbs Ensemble;105
9.1;1. Introduction;105
9.2;2. The phase-space density;107
9.3;3. The classical Liouville theorem;110
9.4;4. The density matrix;116
9.5;5. The quantum Liouville theorem;122
10;CHAPTER IV. Probabilities from Dynamics;127
10.1;1. Dynamical images of events;127
10.2;2. Observational equivalence;131
10.3;3. The classical accessibility postulate;134
10.4;4. The quantum accessibility postulates;138
10.5;5. The equilibrium ensemble;143
10.6;6. Coarse-grained ensembles;149
10.7;7. The consistency condition;155
10.8;8. Transient states;162
11;CHAPTER V. Boltzmann Entropy;166
11.1;1. Two fundamental properties of entropy;166
11.2;2. Composite systems;172
11.3;3. The additivity of entropy;178
11.4;4. Large systems and the connection with thermodynamics;184
11.5;5. Equilibrium fluctuations;191
11.6;6. Equilibrium fluctuations in a classical gas;197
11.7;7. The kinetic equation for a classical gas;204
11.8;8. Boltzmann's H theorem;210
12;CHAPTER VI. Statistical Entropy;219
12.1;1. The definition of statistical entropy;219
12.2;2. Additivity properties of statistical entropy;227
12.3;3. Perpetual motion;232
12.4;4. Entropy and information;237
12.5;5. Entropy changes in the observer;242
13;Solutions to Exercises;250
14;Index;260
15;OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY;272
