Statistical physics II. Nonequilibrium statistical mechanics. Rev. transl. of the rev. orig. Jap. ed.
type: Item
instance of: scholarly article
title: Statistical physics II. Nonequilibrium statistical mechanics. Rev. transl. of the rev. orig. Jap. ed.
zbMATH Open document ID: 0757.60109
author: Ryogo Kubo
author: Morikazu Toda
author: Natsuki Hashitsume
published in: Springer Series in Solid-State Sciences
publication date: 1992-09-18T00:00:00Z
review text: The second edition of Statistical Physics II has no essential additions or changes except some corrections for improving the presentation. It is a perfect introduction in nonequilibrium statistical mechanics which covers the fundamental topics with appropriate physical examples and applications. The Chapters 1 and 2 are an excellent exposition of the Brownian motion and well-balanced presentation of stochastic processes. Chapter 3 provides a link between the formalism developed in Chapters 1, 2 and the Chapters 4, 5 on the basis of phenomenological theories of relaxation processes from nonequilibrium to equilibrium states. In Chapter 4 the theory of linear response is presented. This theoretical method is known as Kubo's response theory which allows to derive from microscopic physics the relaxation and response functions for linear irreversible processes. The conceptional and mathematical difficulties of the linear-response theory are discussed in Section 4.7. In particular, it contains a respond to ``van Kampen's objection'' to this theory. Instructive remarks on the subject the reader can find in the review of the first edition by \textit{J. L. Lebowitz} in J. Stat. Phys. 44, 697 (1986). The mathematical foundation of the linear-response theory for quantum lattice systems with finite-range potentials and integrable space clustering are contained in the recent paper by \textit{G. Goderis, A. Verbeure} and \textit{P. Vets} [Commun. Math. Phys. 136, 265 (1991)]. The last Chapter 5 contains an extensive discussion of quantum field theoretical methods in statistical mechanics, i.e., diagrammatic techniques for Green's functions. It is a popular important method in many-body theory and solid-state physics. The book can be highly recommended as a good introduction to nonequilibrium statistical mechanics with the accent on the physical applications of the linear theory.
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 82-01
Mathematics Subject Classification ID: 82B03
zbMATH DE Number: 52081
zbMATH Keywords: relaxation processes from nonequilibrium to equilibrium states
zbMATH Keywords: response theory
zbMATH Keywords: quantum lattice systems
zbMATH Keywords: nonequilibrium statistical mechanics
reviewed by: V. A. Zagrebnov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 52081