Mathematical Foundations of Classical Statistical Mechanics

by Petrina; D.Ya.

• ISBN13: 9780415273541
• ISBN10: 0415273544
• eBook ISBN(s): 9781040214664
• Edition: 2nd
• Format: Hardcover
• Copyright: 2002-04-11
• Publisher: CRC Press
• More Book Details

Summary

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 moresystematically, 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.

Author Biography

D. Ya. Petrina is a full Professor, Corresponding Member of the National Academy of Sciences of Ukraine, Head of the Department of Mathematical Methods of Statistical Mechanics of Kiev Institute of Mathematics.

Table of Contents

Problem for the BBGKY Hierarchy

Equilibrium States

Canonical Ensemble

Equilibrium States

Grand Canonical Ensemble

Thermodynamic Limit for Non-equilibrium Systems

Stationary Solutions of the BBGKY Hierarchy of Equations

Existence of the Hamiltonian Dynamics of Infinitely Many Particles

References

Index

Table of Contents provided by Publisher. All Rights Reserved.