This chapter discusses several statistical mechanical theories that are strongly positioned in the historical sweep of the theory of liquids. They are chosen for inclusion here on the basis of their potential for utility in analyzing simulation calculations, and their directness in connecting to the other fundamental topic discussed in this book, the potential distribution theorem. Therefore tentacles can be understood as tentacles of the potential distribution theorem. From the perspective of the preface discussion, the theories presented here might be useful for discovery of models such as those discussed in Chapter 4. These theories are a significant subset of those referred to in Chapter 1 as “… both difficult and strongly established …” (Friedman and Dale, 1977), but the present chapter does not exhaust the interesting prior academic development of statistical mechanical theories of solutions. Sections 6.2 and 6.3 discuss alternative views of chemical potentials, namely those of density functional theory and fluctuation theory.

The MM and KS expansions

The Mayer–Montroll (Mayer and Montroll, 1941) and Kirkwood–Salsburg (Kirkwood and Salsburg, 1953) expansions are storied parts of basic statistical thermodynamics (Stell, 1985), but have been neglected for practical purposes because of a lack of recognition of how simple and simplifying they can be.

We introduce results with the specific example of a hard-core solute that was previously considered in Section 4.3. The hard-core results give perspective for a direct generalization to more realistic interactions.