A New Approach to the Theory of Classical Fluids. III

A classical system enclosed in a finite volume and exerted by external forces is treated in quite a general way. The main results, which m~y be applicable to solids as well as to fluids, are as follows. Exact integral equations are found for the one-and two-particle distribution functions. Some thermodynamic functions are expressed in terms of these distribution functions. It is shown that there exist variational principles saying that the grand partition function is to be maximum with respect to the variations in the one-and two-particle distribution functions. Variational principles are found also for the Helmholtz free energy. It is suggested that Mayer's theory of condensation may in fact give the end point of the metastable gaseous state. It is pointed out that the hyper-netted chain approximation, proposed previously by one of the present authors, has a meaning in solids as well as in fluids. * The one-particle distribution function will be denoted simply as p(r).