An introduction to statistical mechanics is an important part of any good undergraduate physical chemistry course. Most standard textbooks, however, provide only minimal coverage focusing on the partition function for the ideal gas and its application to chemical equilibrium. This elegant new book by Benjamin Widom provides an attractive alternative for those faculty and students who want to go further.

To demonstrate the power of statistical mechanics, Widom bypasses the formal development of ensemble theory that is a part of most graduate courses to concentrate on applications. He begins with the Boltzmann distribution, making it plausible by showing that it is consistent with the more familiar Maxwell distribution of velocities and with the barometric distribution. The canonical partition function appears naturally as the normalization constant. After deriving the connections between the partition function and thermodynamic functions he applies the theory to a broad variety of problems.

Chapters 2 and 3 treat ideal polyatomic gases and chemical equilibrium at a level comparable to that found in most undergraduate physical chemistry texts. Chapter 4 is an exposition of the theory of the ideal harmonic crystal in the Debye approximation. Since the mathematics is the same, the chapter concludes with a brief discussion of blackbody radiation. Chapter 5 completes the thermodynamic connection by showing how statistical mechanics provides a microscopic interpretation of the third law.

The last half of the book provides an introduction to the statistical mechanics of strongly interacting systems: non-ideal gases and liquids. Chapter 6 derives the expression for the second virial coefficient and examines some of its properties, while Chapter 7 introduces the radial distribution function, the equation of state of a liquid, and gives a concise introduction to modern computer simulation methods, both molecular dynamics and Monte Carlo. The book concludes with a look at quantum ideal gases, which requires the use of the grand canonical ensemble.

As an undergraduate I learned statistical mechanics from Frank Andrews's lovely little book, Equilibrium Statistical Mechanics (Wiley, 1963, 2nd edition, 1975), which is now a bit dated. Widom has written a volume of comparable scope that shows students the beauty and power of the theory as well as some of its most important contemporary applications. The sections on molecular dynamics and Monte Carlo methods are among the best concise introductions to those techniques that I have read. The prose is clear and erudite reflecting the scientific and personal style of the author. I have had the pleasure of hearing Ben Widom lecture on a number of occasions, and I can almost hear his voice as I read this book.

This book should be in the hands of everyone who teaches undergraduate physical chemistry to provide a model for what can be taught in that course beyond the material contained in the standard textbooks. Graduate students and faculty who need to learn statistical mechanics can hardly find a better introduction. Even those who regularly teach a graduate course in this area will get some new ideas and inspiration from one of the leading practitioners of the field. For completeness, I must add that the book has one weakness. Although there are excellent in-chapter exercises with solutions, there are no end-of-chapter problems. Since there are many sources of good problems, this is a minor flaw in an otherwise wonderful book.