Statistical mechanics of stationary states. VI. Hydrodynamic fluctuation theory far from equilibrium

Fluctuating hydrodynamics is extended to the nonequilibrium regime. Two modifications to the equilibrium theory are made: (i) The dynamics of the fluctuations are linearized about a nonequilibrium steady state (NESS). (ii) The stochastic behavior of the random forces (noise) is equilibriumlike, satisfying a local fluctuation-dissipation theorem. Thus, the noise correlations depend on position through their dependence on the NESS temperature, chemical potential, and velocity. It is shown that this is sufficient to give the results of our earlier microscopic analysis and sheds new light on their interpretation. A microscopic justification of the fluctuating hydrodynamic procedure is offered.