Jancel / Ter Haar Foundations of Classical and Quantum Statistical Mechanics

International Series of Monographs in Natural Philosophy
1. Auflage 2013
ISBN: 978-1-4831-8626-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 440 Seiten, Web PDF

Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.

Autoren/Hrsg.

Jancel, R.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Foundations of Classical and Quantum Statistical Mechanics;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Preface to the English edition;12
7;General Introduction;16
8;PART I: Ergodic Theory;34
8.1;CHAPTER I. The Ergodic Theory in Classical Statistical Mechanics;36
8.1.1;I. Statistical Ensembles of Classical Systems;36
8.1.2;II. Ergodic Theorems in Classical Mechanics;44
8.1.3;III. The Hypothesis of Metric Transitivity;54
8.2;CHAPTER II. Quantum Mechanical Ensembles. Macroscopic Operators;74
8.2.1;I. Statistical Ensembles of Quantum Systems;74
8.2.2;II. Macroscopic Operators;86
8.3;CHAPTER III. The Ergodic Theorem in Quantum Statistical Mechanics;93
8.3.1;I. The Ergodic Problem in Quantum Mechanics;93
8.3.2;II. The First Quantum Ergodic Theorem;95
8.3.3;III. The Second Quantum Ergodic Theorem;98
8.3.4;IV. The Proofs of von Neumann and Pauli–Fierz;106
8.4;CHAPTER IV. Probability Quantum Ergodic Theorems;130
8.4.1;I. Comments on the Quantum Ergodic Theory;130
8.4.2;II. First Probability Ergodic Theorem (Jancel, 1955a);132
8.4.3;III. The Macroscopic Probability Ergodic Theorem;138
8.4.4;IV. Statistical Properties of Macroscopic Observables. Comparison with Classical Theory;149
8.4.5;V. Relations between Microcanonical, Canonical and Grand-Canonical Ensembles;167
9;PART II: H-Theorems;180
9.1;Introduction;182
9.2;CHAPTER V. H-Theorems and Kinetic Equations in Classical Statistical Mechanics;187
9.2.1;I. Mechanical Reversibility and Quasi-Periodicity;187
9.2.2;II. Coarse-Grained Densities and the Generalised H-Theorem;196
9.2.3;III. Transition Probabilities and Boltzmann's Equation;205
9.2.4;IV. Stochastic Processes and H-Theorems;220
9.2.5;V. Integration of the Liouville Equation;229
9.2.6;VI. Prigogine's Theory of Irreversible Processes;258
9.3;CHAPTER VI. H-Theorems and Kinetic Equations in Quantum Statistical Mechanics;279
9.3.1;I. Fine- and Coarse-grained Densities in Quantum Mechanics;280
9.3.2;II. The H-Theorem for an Ensemble of Quantum Systems;290
9.3.3;III. The Kinetic Equation and Irreversible Processes;293
9.3.4;IV. Boltzmann's Equation and Stochastic Processes in Quantum Theory;309
9.3.5;V. Zwanzig's Method;319
9.4;CHAPTER VII. General Conclusions. Macroscopic Observation and Quantum Measurement;336
9.4.1;I. Applications of Statistical Mechanics;337
9.4.2;II. Quantum Measurement and Macroscopic Observation;343
10;Appendix I;349
10.1;1. Historical review of ergodic theory;349
10.2;2. Birkhoff's theorem;352
10.3;3. Notes on the metric transitivity of hypersurfaces;355
10.4;4. Structure functions in classical statistical mechanics;363
11;APPENDIX II: Probability Laws in Real n-Dimensional Euclidean Space;370
11.1;1. The unit hypersphere in n-dimensional space;370
11.2;2. The unit hypersphere in 2n-dimensional space;373
11.3;3. Probability laws for the quantities D(v)ii and µ(a)ii;377
12;APPENDIX III A: Ehrenfests' Model;391
12.1;1. The function H(Z, t) and the "H-curve";391
12.2;2. Ehrenfests' model;392
12.3;3. Transition probabilities and the fundamental equation;393
12.4;4. Stationary distribution;395
12.5;5. Properties of the ".s-curve";397
12.6;6. Calculation of P(n\m, s);398
13;APPENDIX III B: Notes on the Definition of Entropy;401
14;APPENDIX IV: Note on Recent Developments in Classical Ergodic Theory;403
14.1;I. The Concept of an Abstract Dynamic System;404
14.2;II. Asymptotic Properties of Abstract Dynamic Systems;406
14.3;III. Entropy and K-systems;414
15;Bibliography;420
16;Index;434