Entropy power functional theory for Brownian many-body dynamics

We present a formally exact variational scheme for the overdamped Brownian dynamics of pairwise interacting many-body systems in general spatiotemporal nonequilibrium. A joint free power minimization principle determines instantaneously the one-body current and the global interparticle distance flux. The intrinsic free power functional splits into entropic and energetic rates, where the latter are treated explicitly. The adiabatic contribution to the entropy rate is the time derivative of the equilibrium entropy metadensity functional. Genuine nonequilibrium effects originate from a universal entropy superpower functional. Two continuity equations close the dynamical description.