A lower bound on the third virial coefficient for a system of arbitrary hard convex particles

Abstract

In this Brief Communication a lower bound on the third virial coefficient for a system of arbitrary hard convex particles is determined, using a result from integral geometry. The bound is a simple function of the volumes, surface areas, and integrals of the mean curvature of the particles. Applied to a system of identical balls, the ratio of the exact result to the lower bound is 1.1298... . The bound does not become trivial (i.e., zero or negative) for systems of particles of zero volumes provided that they have positive surface areas.