Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. III. Cluster Analysis of the Renormalized Interactions and a Second Diagrammatic Representation of the Correlation Functions

Abstract

This is the third of a series of papers that presents a kinetic theory of fluctuations in equilibrium classical fluids that makes extensive use of diagrammatic techniques in its development and that will facilitate the use of diagrammatic techniques in the derivation of approximate kinetic theories. The fundamental fluctuating quantity in the theory is f(R,P), the density of particles (atoms) at points in single particle phase space, and the time correlation functions for fluctuations of this quantity from its average are the quantities that the theory is designed to calculate. In this paper, we start with graphical diagrammatic expressions for the correlation functions and for closely related response functions, developed in paper II, and analyze the cluster properties of the various renormalized interactions that appear in the theory. This allows us to derive a second diagrammatic formulation that has many similarities to the Mayer cluster theory for equilibrium correlation function. This second formula...