ANALYTIC REPRESENTATION OF THE EQUATION OF STATE IN CLASSICAL STATISTICAL-MECHANICS

For a system of classical particles with short-range pairwise interact ions, analytic representations of the spherically-symmetrical (uniform ) compression modulus are constructed in terms of convergent series in the usual and complementary densities and in terms of contour integra ls. Similar representations are given for the equation of state and th e specific logarithm of the configuration integral. The uniform compre ssion modulus, which appears to be single-valued in a vicinity of the phase transition, suffices to determine all of the interesting thermod ynamic quantities. The techniques which we develop are tested by appli cation to an exactly solvable model, the ''Van der Waals substance,'' which is a model ''substance'' whose exact equation. of state is given by the Van. der Waals equation.