On the Langevin formalism for nonlinear and nonequilibrium hydrodynamic fluctuations

The Landau-Lifshitz method of fluctuating hydrodynamics is generalized to the cases of nonlinear and nonequilibrium fluctuations. For a simple one-component fluid, the multiplicative random fluxes are constructed by using universal Gaussian variables with variances independent of the specific parameters of a fluid. It is shown that the nonlinear Langevin formalism proposed is equivalent to the approach based on the hydrodynamic Fokker-Planck equation derived earlier by statistical-mechanical methods. Then, the scheme is extended to the case of two-component fluids, where cross effects must be taken into account. In conclusion, the connection of the present formalism with the Keizer approach to nonequilibrium fluctuations is discussed.