Foundations of Classical and Quantum Statistical Mechanics
International Series of Monographs in Natural Philosophy
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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.
Table of Contents
Preface
Preface to the English Edition
General Introduction
Part I. Ergodic Theory
Chapter I. The Ergodic Theory in Classical Statistical Mechanics
I. Statistical Ensembles of Classical Systems
II. Ergodic Theorems in Classical Mechanics
III. The Hypothesis of Metric Transitivity
Chapter Ii. Quantum Mechanical Ensembles. Macroscopic Operators
I . Statistical Ensembles of Quantum Systems
II. Macroscopic Operators
Chapter III. The Ergodic Theorem in Quantum Statistical Mechanics
I. The Ergodic Problem in Quantum Mechanics
II. The First Quantum Ergodic Theorem
III. The Second Quantum Ergodic Theorem
IV. The Proofs of Von Neumann and Pauli-Fierz
Chapter IV. Probability Quantum Ergodic Theorems
I. Comments on the Quantum Ergodic Theory
II. First Probability Ergodic Theorem
III. The Macroscopic Probability Ergodic Theorem
IV. Statistical Properties of Macroscopic Observables. Comparison with Classical Theory
V. Relations between Microcanonical, Canonical and Grand-Canonical Ensemble
Part II. H-Theorems
Introduction
Chapter V. H-Theorems and Kinetic Equations in Classical Statistical Mechanics
I. Mechanical Reversibility and Quasi-Periodicity
II. Coarse-Grained Densities and the Generalized H-Theorem
III. Transition Probabilities and Boltzmann's Equation
IV. Stochastic Processes and H-Theorems
V. Integration of the Liouville Equation
VI. Prigogine's Theory of Irreversible Processes
Chapter VI. H-Theorems and Kinetic Equations in Quantum Statistical Mechanics
I. Fine- and Coarse-Grained Densities in Quantum Mechanics
II. The H-Theorem for an Ensemble of Quantum Systems
III. The Kinetic Equation and Irreversible Processes
IV. Boltzmann's Equation and Stochastic Processes in Quantum Theory
V. Zwanzig's Method
Chapter Vii. General Conclusions. Macroscopic Observation and Quantum Measurement
I. Applications of Statistical Mechanics
II. Quantum Measurement and Macroscopic Observation
Appendix I
1. Historical Review of Ergodic Theory
2. Birkhoff's Theorem
3. Notes On the Metric Transitivity of Hypersurfaces
4. Structure Functions in Classical Statistical Mechanics
Appendix II. Probability Laws in Real n-Dimensional Euclidean Space
1. The Unit Hypersphere in n-Dimensional Space
2. The Unit Hypersphere in 2n-Dimensional Space 340
3. Probability Laws for the Quantities Dii(y) and µij(α)
Appendix III A. Ehrenfests' Model
1. The Function H(Z, t) and the "H-Curve"
2. Ehrenfests' Model
3. Transition Probabilities and the Fundamental Equation
4. Stationary Distribution
5. Properties of the "Δs-Curve"
6. Calculation of P(n│m, s)
Appendix III B. Notes on the Definition of Entropy
Appendix IV. Note on Recent Developments in Classical Ergodic Theory
I. The Concept of an Abstract Dynamic System
II. Asymptotic Properties of Abstract Dynamic Systems
1. Definitions
2. Asymptotic Properties
III. Entropy and K-Systems
1. Measurable Decompositions
2. Entropy
3. K-Systems
Bibliography
Index
Product details
- No. of pages: 440
- Language: English
- Copyright: © Pergamon 1963
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483186269
About the Author
R. Jancel
About the Editor
D. ter Haar
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