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The Langevin formalism that describes fluctuations about thermodynamic equilibrium is extended to study hydrodynamic nonequilibrium steady states. The limitations of our generalization are discussed as well as the connection between experimental and theoretical quantities which is more subtle than in equilibrium. The spectrum for Brillouin scattering from a fluid in a shear flow or temperature gradient is simply obtained by Langevin methods. The latter problem exhibits an asymmetry in the height of the peaks inversely proportional to the square of the scattering wave vector. We also construct a microscopic ensemble that is applicable to a variety of hydrodynamic nonequilibrium steady states, and then verify for a particular model that our extension of the Langevin method agrees with a fully microscopic calculation.
Tremblay et al. (Sun,) studied this question.