Conditional entropy; an alternative derivation of the pair correlation function for simple classical fluids

TL;DR

This paper introduces a variational method based on conditional entropy to derive the pair correlation function in simple classical fluids, unifying existing approximations like hypernetted chain and Percus-Yevick.

Contribution

It provides a novel derivation of the pair correlation function using a variational approach and conditional entropy, connecting it to established integral equations.

Findings

Derivation of a non-linear integral equation for g(R)

Unification of hypernetted chain and Percus-Yevick approximations as limits

New variational framework for classical fluid correlations

Abstract

We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect to a given pair (1,2), and the definition of a conditional entropy $\sigma$(3,..., N /1, 2). An additivity assumption of $\sigma$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1, 2) allows deriving the pair probability p(1,2). We then focus onto the case of simple classical fluids, which leads to an integral, non-linear equation that formally allows computing the pair correlation function g(R). That equation admits the one resulting from the hyper netted chain approximation (and the Percus-Yevick approximation) as a limit case.