EQUATIONS OF FLUCTUATING NONLINEAR HYDRODYNAMICS FOR NORMAL FLUIDS

The full set of fluctuating nonlinear hydrodynamic equations for normal fluids is derived from the conventional Langevin equations extended to include multiplicative noise. The equations describing the set of conserved variables (the mass density rho, the momentum density g, the energy density epsilon) agree with those found by Morozov for a case of a driving free energy which is a local function of the hydrodynamic variables. We show here that if the standard form of the hydrodynamic equations is to hold in the absence of noise, then the driving free energy must be a local function of g and epsilon, but it may have to be a nonlocal function of the mass density.