An Entropic Approach To Classical Density Functional Theory

TL;DR

This paper presents a novel entropic inference framework for classical density functional theory (DFT), connecting entropy maximization with the variational principle to model inhomogeneous fluids at equilibrium.

Contribution

It introduces an entropic inference approach to derive DFT, providing a new perspective and approximation scheme for slowly varying density models.

Findings

Entropic inference reproduces the variational principle of DFT.

A new approximation scheme for slowly varying densities is discussed.

The method introduces an intermediate entropy and trial density distributions.

Abstract

The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids at thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when information about expected density of particles is imposed. This process introduces an intermediate family of trial density-parametrized probability distributions, and consequently an intermediate entropy, from which the preferred one is found using the method of Maximum Entropy (MaxEnt). As an application, the DFT model for slowly varying density is provided, and its approximation scheme is discussed.