Maximum Entropy approach to a Mean Field Theory for Fluids

TL;DR

This paper develops a mean field theory for classical fluids using a maximum entropy approach, generalizing the Bogoliubov variational principle and applying it to Argon gas with results compared to experiments.

Contribution

It introduces a novel application of maximum entropy to derive a mean field theory for fluids, extending the Bogoliubov variational principle.

Findings

Numerical results for Argon gas align well with experimental data.

Generalization of the Bogoliubov variational principle for fluid systems.

Application of maximum entropy to density functional theory.

Abstract

Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first problem. Here we explore its use to tackle the second problem. We show how this use of maximum entropy leads to the Bogoliuvob variational principle which we generalize, apply to density functional theory, and use it to develop a mean field theory for classical fluids. Numerical calculations for Argon gas are compared with experimental data.