Maximum entropy approach to the theory of simple fluids

TL;DR

This paper applies the Maximum Entropy method to approximate the behavior of simple fluids, improving upon traditional variational approaches by accounting for soft-core potentials through a mixture of hard-sphere distributions.

Contribution

It introduces a novel application of the Maximum Entropy method to fluid theory, providing more accurate approximations of interatomic potentials and radial distribution functions.

Findings

ME method yields results matching Bogoliubov variational method

Enhanced description of soft-core potentials via mixture distributions

Radial distribution function for Argon agrees better with simulations

Abstract

We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard spheres; ME is used to select an optimal value of the hard-sphere diameter. These results coincide with the results obtained using the Bogoliuvob variational method. A second more complete use of the ME method leads to a better descritption of the soft-core nature of the interatomic potential in terms of a statistical mixture of distributions corresponding to hard spheres of different diameters. As an example, the radial distribution function for a Lennard-Jones fluid (Argon) is compared with results from molecular dynamics simulations. There is a considerable improvement over the results obtained from the Bogoliuvob principle.