A nonlinear diffusion approximation for a previously derived master equation describing an inhomogeneous Boltzmann gas in a lumped phase space is proposed. A fluctuating kinetic equation is obtained which differs from the usual Langevin equations in three essential properties: the drift and random force are nonlinear, the random noise obeys a generalized fluctuation-dissipation theorem, and there is no reference to equilibrium. Relations with other approaches to hydrodynamic fluctuations are discussed.

• Received 7 December 1978

DOI:https://doi.org/10.1103/PhysRevA.21.1039