Mathematical Foundations of Classical Statistical Mechanics (Advanced Studies in Contemporary Mathematics)

✍ Scribed by D.Ya. Petrina, V.I. Gerasimenko, P V Malyshev

• Publisher: CRC Press
• Year: 2002
• Tongue: English
• Leaves: 349
• Edition: 1
• Category: Library

✦ Synopsis

This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface to the Second Edition
Preface to the First Edition
Introduction
Chapter 1: Dynamics of Systems of Finitely Many Particles
1. Classical Mechanics of Hamiltonian Systems
2. Evolution Operator
3. Liouville Equation
Bibliographical Notes
Chapter 2: Cauchy Problem for the BBGKY Hierarchy
4. BBGKY Hierarchy
5. Formal Solutions of the Cauchy Problem for the BBGKY Hierarchy
6. Rigorous Construction of the Solution of the Cauchy Problem for the BBGKY Hierarchy of Equations in the Case of Summable Initial Data
Bibliographical Notes
Chapter 3: Equilibrium States. Canonical Ensemble
7. Stationary Liouville Equation. Equilibrium Gibbs States
8. Existence of Solutions of the Kirkwood–Salsburg Equations
9. Existence of the Limit Correlation Functions
10. Uniqueness of the Limit Correlation Functions
Bibliographical Notes
Chapter 4: Equilibrium States. Grand Canonical Ensemble
11. Equations for Correlation Functions
12. Kirkwood–Salsburg Operator: Spectral and Topological Properties
13. Stable and Superstable Interactions
14. Equilibrium Correlation Functions for Arbitrary Values of Activity
15. Thermodynamic Limit for Arbitrary Values of Activity
16. Gibbs Distributions
Bibliographical Notes
Chapter 5: Thermodynamic Limit for Nonequilibrium Systems
17. Solutions of the Cauchy Problem for the BBGKY Hierarchy of Equations in the Space of Sequences of Bounded Functions
18. Evolution of a Three-Dimensional System of Hard Spheres
19. Boltzmann–Grad Limit for the Solutions of the BBGKY Hierarchy
Bibliographical Notes
Appendix 1: Stationary Solutions of the BBGKY Hierarchy of Equations
Appendix 2: Existence of the Hamiltonian Dynamics of Systems of Infinitely Many Particles
REFERENCES
INDEX