2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95931We 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.10 pages, 1 figure, to be submitted to Journal of Physics A: Mathematical and GeneralStatistical Mechanicstext