Statics and dynamics of inhomogeneous liquids via the internal-energy functional

TL;DR

This paper develops a variational framework for inhomogeneous liquids using internal-energy functionals, enabling the study of both static properties and dynamics including heat transport and thermal diffusion.

Contribution

It introduces a novel variational formulation with the one-body density and entropy as trial fields, extending dynamical density functional theory to include entropy dynamics.

Findings

Functional splits into entropic, external, internal energetic parts

Transforms common free energy functionals into internal energy functionals

Generalizes dynamical density functional theory to include entropy dynamics

Abstract

We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a functional of both distributions, that it is minimal in equilibrium, and that the minimizing fields are those at equilibrium. The functional splits into a sum of entropic, external energetic and internal energetic contributions. Several common approximate Helmholtz free energy density functionals, such as the Rosenfeld fundamental measure theory for hard sphere mixtures, are transformed to internal energy functionals. The variational derivatives of the internal energy functional are used to generalize dynamical density functional theory to include the dynamics of the microscopic entropy distribution, as is relevant for studying heat transport and thermal diffusion.