Power functional theory for Newtonian many-body dynamics.

We construct a variational theory for the inertial dynamics of classical many-body systems out of equilibrium. The governing (power rate) functional depends on three time- and space-dependent one-body distributions, namely, the density, the particle current, and the time derivative of the particle current. The functional is minimized by the true time derivative of the current. Together with the continuity equation, the corresponding Euler-Lagrange equation uniquely determines the time evolution of the system. An adiabatic approximation introduces both the free energy functional and the Brownian free power functional, as is relevant for liquids governed by molecular dynamics at constant temperature. The forces beyond the Brownian power functional are generated from a superpower (above the overdamped Brownian) functional.