Mathematical Foundations of Classical Statistical Mechanics

ISBN-13: 9780415273541 / Angielski / Twarda / 2002 / 352 str.

D.Ya. Petrina;V.I. Gerasimenko;P V Malyshev

Opis

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.

This text investigates systems of an infinite number of particles, in particular, the justification of the procedure of thermodynamic limit transition. This is the first detailed study of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. The authors' updates in this edition reflect developments in theory over the last ten years. The authors also simplified certain sections, presenting them more systematically and add new references. The book is useful to postgraduate students and researchers in theoretical physics and mathematics.

Recenzje

"[A] good reference in which many classical and profound results of both equilibrium and nonequilibrium statistical mechanics are collected and presented in a unified way."
- SIAM Review, Vol. 46, No. 1

Spis treści

Problem for the BBGKY Hierarchy. Equilibrium States. Canonical Ensemble. Equilibrium States. Grand Canonical Ensemble. Thermodynamic Limit for Non-equilibrium Systems. Appendix 1: Stationary Solutions of the BBGKY Hierarchy of Equations. Appendix 2: Existence of the Hamiltonian Dynamics of Infinitely Many Particles. References. Index.

O autorze

D.Ya. Petrina, V.I. Gerasimenko, P V Malyshev