The Lennard-Jones lecture: the statistical mechanics of small systems

Abstract

The statistical mechanics of a small system can be obtained in the form of the virial expansion of the grand potential in powers of the activity or of the mean number of molecules in the system. It is shown how the latter expansion differs from that found in infinitely large homogeneous systems. Series of finite length are obtained by expanding the grand partition function and these are often more useful; they lead simply, for example, to exact results for the distribution of hard rods on a line of finite length. Approximate but closed expressions for the local density etc. can be obtained by summing some of the terms of the virial expansions. If these are to be useful in small but complicated systems, such as the pores of a zeolite, it is preferable that they involve only the one-body distribution function (or local density) and its gradients. Some progress in this direction is described.