Power functional theory for Brownian dynamics

TL;DR

This paper extends classical density functional theory to non-equilibrium Brownian systems by introducing a dynamical functional framework, enabling systematic study of far-from-equilibrium dynamics.

Contribution

It generalizes DFT to include non-equilibrium dynamics through a variational principle based on free power functional, bridging equilibrium and dynamic regimes.

Findings

Recovers standard DFT in equilibrium limit

Derives a closed equation of motion for Brownian systems

Enables systematic approximation beyond adiabatic regime

Abstract

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this `free power' functional with respect to the microscopic one-body current yields a closed equation of motion. In the equililibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.