Introductory Statistical Mechanics

Abstract

There exist so many textbooks on statistical thermodynamics - what is then the point of having a new one? Well, any lecturer who delivers a university course on this subject will have experienced that it is fairly difficult to explain the basic concepts, such as entropy and the probabilistic approach to it, in a way that is easily comprehensible and at the same time encompasses the necessary generality and rigour. In fact, many of the existing textbooks are either rather formal on many aspects and not written in an easily comprehensible pedagogically appealing style, or they are simply far too voluminous to easily form the basis of a course. In these respects the present book is very different - the authors, Roger Bowley and Mariana Sanchez, make a real effort to introduce the subject in a step-by-step-fashion that can easily be followed by any student who has some knowledge of elementary classical mechanics and basic quantum mechanics. Starting out with an elementary discussion of the main concepts of phenomenological thermodynamics, and the basic terms and notions that are introduced there, a short and very elementary treatise of the necessary concepts of probability theory follow. Then the basic ideas of statistical mechanics are described and immediately illustrated by simple but relevant applications, like non-interacting spins on a lattice, or the entropic elasticity of a rubber band. Only after the reader has been familiarized in this way with the idea of counting the thermodynamic probability W and the entropy S via Boltzmann's formula (S = kB ln W ), does an exposition of the canonical ensemble follow. In this chapter, close contact with elementary quantum mechanics is maintained by calculating partition functions of quantum particles in one- and three-dimensional confining boxes, and proceeding then to diatomic molecules. Then the particular aspects of dealing with the statistical mechanics of many identical particles are developed, giving very nice application examples both for bosons and for fermions (e.g. the cosmic background radiation is dealt with in conjunction with Planck's distribution, and electrons in white dwarfs are treated as example of Fermi systems, etc). These examples are not just schematic, but show comparisons to carefully selected experimental data. And throughout the whole text one can find many problems that illustrate the concepts nicely and help significantly to deepen the reader's understanding. The final three chapters (11-13) deal with some aspects of phase transitions. Again both the discussion of the basic description of first-order phase transitions and the mean-field treatment of the Ising model are written in the same easily comprehensive style as the whole book. However, I do not like so much the very last chapter on Ginzberg-Landau theory: here more motivating comments or a derivation (such as going from an inhomogeneous formulation of molecular field theory on a lattice to the continuum by expanding differences in terms of differentials) would be needed to make this section as nicely comprehensible as the other sections, and some parts (e.g. the sections on the Ginzberg criterion and on the surface tension) I find too sketchy. But this is clearly a minor detail, and as a whole the concept of this book is very well thought through, and the exposition very clear. The value of the book is further enhanced by several useful appendices, answers to the problems, and a bibliography which is a good mix of historical landmarks and recent developments.