Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

TL;DR

This paper clarifies whether dynamical density functional theories for Brownian particles should include stochastic noise, showing that both stochastic and deterministic forms are justifiable depending on the density definition.

Contribution

It elucidates the conditions under which stochastic or deterministic dynamical density functional equations are appropriate for Brownian fluids.

Findings

Both stochastic and deterministic equations are valid for the one-body density.

The choice depends on whether the density is ensemble-averaged or coarse-grained.

The paper resolves confusion in the literature regarding the nature of the equations.

Abstract

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.