||Statistical mechanics is the physical theory of the thermal properties of macroscopic systems. It relates these properties to the mechanics of the constituent microscopic particles. Owing to the enormous number of particles, their average behaviour is well defined and this is what determines their thermal properties. This theory was originally formulated about a century ago by L Boltzmann and J Gibbs. However, since these early beginnings the theory has been extended and developed considerably. In particular, equilibrium statistical mechanics, which is the subject of this book, has been put on a much firmer mathematical basis. Nevertheless the subject is normally still taught in a rather traditional fashion.
This book is an introduction to the subject with more emphasis on the mathematical structure than is usual. In particular, it is emphasized that it is essential that the number of particles in the system is large. This means that one has to take the thermodynamic limit where the number of particles and the volume of the system tend to infinity in such a way that the particle density remains constant. Also, in particular in Part I about thermodynamics, the convexity of many of the thermodynamic functions is shown to play a central role. This important property is usually completely ignored in standard texts, which makes the definition of thermodynamic potentials often somewhat obscure.
The greater reliance on mathematical concepts naturally means that the student is assumed to be familiar with some basic undergraduate mathematics. Specifically, the student is assumed to be familiar with the basic concepts of real analysis (continuous functions, open and closed sets, lim inf and lim sup) and of probability theory (random variables and distribution functions). (There is, however, an appendix about probability theory at the end of the book.) More non-standard theory is developed in the text; there is a chapter in Part I devoted to some properties of convex functions (as well as an appendix with more advanced theory) and a chapter in Part II which is an introduction to the theory of large deviations. However, the proofs of theorems in these chapters are not essential and, by retaining the dimensional factors in most formulae, I expect that this book will still be suitable for physics students.