ARCHER, A.J. and RAUSCHER, M., 2004. Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic? Journal of Physics A: Mathematical and General, 37 (40), pp. 9325 - 9333.
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.