Short Book Reviews, International Statistical Institute, Vol. 5, No. 3 – December 1985
Entropy, Large Deviations, and Statistical Mechanics,
R. S. Ellis. New York: Springer-Verlag, 1985, pp. xiv + 364 pp. DM 184.00.
This book is about the relation between the probabilistic theory of large deviations and statistical mechanics, in particular the occurrence of phase transitions, entropy being a connecting concept. It provides a crisp and illuminating introduction to these fields and also develops the themes primarily covered in great mathematical detail. It is a strength of the book that the author, rather than aiming to give a very comprehensive account of the extensive subject areas he addresses, has chosen to focus on a limited number of judiciously chosen topics. Thus, the statistical mechanical part consists mainly in a detailed discussion of three main types of models, each treated in one chapter. It is a further advantage of the book that much of the more technical material has been placed separately in the second part of the book. There are interesting connections to the theory of exponential families and to saddle-point approximations and in this relation the exposition of Varadhan’s extension of Laplace’s method deserves special mention. The book fills a lacuna in the literature in a splendid fashion.