Particle Conservation in Dynamical Density Functional Theory

TL;DR

This paper develops an exact adiabatic dynamical density functional theory that accurately predicts particle conservation and interparticle forces in classical fluids, aligning well with simulations for finite, out-of-equilibrium systems.

Contribution

It introduces an exact adiabatic theory ensuring particle number conservation and derives a canonical free energy functional applicable to finite, inhomogeneous systems.

Findings

Erroneous particle number fluctuations are eliminated in the theory.

Excellent agreement with simulations using advanced free energy functionals.

Applicable to both equilibrium and non-equilibrium finite systems.

Abstract

We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.