  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.
