Statistical physics I. Equilibrium statistical mechanics. Rev. transl. from the Japanese ed. by Morikazu Toda and Nobuhiko Saitô.
The appearance of the second edition in the Springer series on solid- state sciences is an indication of the success of the authors' style of presentation of statistical physics addressed first of all to the students. In contrast to many textbooks in statistial physics which are either too long (a very common shortcoming) or too terse (as the excellent Landau and Lifschitz book on Statistical Physics), the authors propose a laconic but rather exhaustive exposition of the general principles of the equilibrium statistical mechanics and a selection of the relevant applications, see Chapters 1-3. But they are only preliminaries; the Chapter 4 ``Phase transitions'', and the Chapter 5 ``Ergodic problems'', are the soul of the book. These chapters have been fully revised for the second edition to take into account contemporary knowledge and recent developments of the theory of phase transitions and of the ergodic behaviour of mechanical systems. As the others, the Chapter 4 is a laconic introduction to the methods of the modern theory of phase transitions appealing the reader to look in the special literature for details. The authors motivated the presence of the Chapter 5 devoted to the ergodic problems by ``their own significance as a branch of physics''. For this edition they fully revised Chapter 5 which now includes, together with classical ergodic theorems and abstract dynamical systems, some recent results on the quantum chaos. Summarizing, as far as the authors had an aim to make this book an elementary introduction to the fundamentals of equilibrium statistical mechanics, focused on basic physical aspects, this aim has been undoubtedly achieved.
scientific article; zbMATH DE number 53035