Using Relative Entropy to Find Optimal Approximations: an Application to Simple Fluids

TL;DR

This paper introduces a maximum relative entropy approach to find optimal probability distribution approximations, demonstrated on simple fluids, improving the modeling of interatomic potentials and matching simulation results.

Contribution

It develops a formalism using relative entropy for optimal distribution approximation and applies it to simple fluids, enhancing the modeling of soft-core interactions.

Findings

Improved approximation of the radial distribution function.

Enhanced equation of state predictions for Lennard-Jones fluids.

Better accounting for soft-core interatomic potentials.

Abstract

We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The "exact" canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations.