Article
Augmented Langevin Approach to Fluctuations in Nonlinear Irreversible Processes
Journal of Statistical Physics
(1985)
Abstract
A Fokker-Planck equation derived from statistical mechanics by M. S. Green [J. Chem. Phys.20:1281 (1952)] has been used by Grabertet al. [Phys. Rev. A21:2136 (1980)] to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker-Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker-Planck equation as that of Grabertet al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker-Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.
Disciplines
Publication Date
February, 1985
DOI
10.1007/BF01010484
Publisher Statement
At the time of publication John Ramshaw was affiliated with the Los Alamos National Laboratory.
Citation Information
J. D. Ramshaw, "Augmented Langevin Approach to Fluctuations in Nonlinear Irreversible Processes," J. Stat. Phys. 38, 669 (1985).