Thermodynamic Consistency and Classical Liquid Structural Theory

Abstract

For classical liquids, with density-independent pair potentials φ(r) which possess a Fourier transform, a full study is made of the Born-Green-Yvon equation which links pair correlations, via the three-particle correlation function g ₃, with the potential. It is shown that the shape of classical liquid structural theory is thereby determined, the pair potential φ(r) being given as the difference between a function in r space involving both g ₃ and φ(r), and a convolution of this same function with the Ornstein-Zernike direct correlation function. Into this equation, a decomposition of the direct correlation function is inserted, which is designed to retain thermodynamic consistency between virial and compressibility routes to the equation of state, when approximations to g ₃ are introduced, as is presently inevitable in analytical work. Some aspects of the procedure proposed are illustrated using the example of the two-dimensional one-component plasma with an interaction satisfying Poisson's equation in two dimensions.

Key Words:

• Direct and three-particle correlation functions