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.