Equilibrium and nonequilibrium statistical mechanics.

*(English)*Zbl 0984.82500
New York, NY: Wiley. xiv, 742 p. (1975).

This is a “textbook” on statistical mechanics intended for graduate students in physics. Perhaps some researchers will find this book a useful reference, especially in the field of nonequilibrium phenomena. The novel feature of the book is the amount of space devoted to the field of nonequilibrium statistical mechanics. This is to be expected, as the Brussels school led by I. Prigogine has made significant contributions in this area. The book consists of three parts. After introducing the general foundations of classical and quantum mechanics in the first part, the author discusses equilibrium phenomena in great detail in the second part. A welcome innovation is the treatment of classical and quantum descriptions side by side. Further, there are two novel chapters in this part of the book, one discussing in some detail the properties of reduced distribution functions for equilibrium system and the other on the theory of renormalization groups in critical phenomena. In the third part of the book, on nonequilibrium phenomena (some 320 pages are devoted to this subject), the successes and limitations of such equations as those of Boltzmann, Fokker-Planck and Vlasov are discussed. A few applications to dilute gases near equilibrium are worked out, such as in the evaluation of transport coefficients. In the succeeding chapters an ambitious programme for a contracted description of nonequilibrium phenomena, starting from the \(N\)-body Liouville equation, is started. Such questions as how the \(L-t\) invariance is broken, starting from the reversible Liouville equation, are considered. Ergodic theory is treated from a physicist’s point of view in an appendix. If one makes a judicious choice of subject matter, this book could be effectively used as a textbook, for instance in a two-semester course on nonequilibrium statistical mechanics. One shortcoming of the book, from the point of view of a North American reviewer, is the absence of problems that would enable one to test whether he had understood the theory presented in the often long chapters. The reviewer would have particularly welcomed problems in the third part of the book. In summary, the physics community will certainly welcome this new contribution to the literature of the field and the author should certainly be congratulated for writing a unified and balanced treatment of equilibrium and nonequilibrium statistical mechanics.

Reviewer: K. S. Viswanathan (MR 53:12405)