Augmented Langevin approach to fluctuations in nonlinear irrversible proceses

Journal Article · Fri Feb 01 04:00:00 EST 1985 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01010484· OSTI ID:5746715

Ramshaw, J D

A Fokker-Planck equation derived from statistical mechanics by M. S. Green (J. Chem. Phys. 20:1281 (1952)) has been used by Grabert et al. (Phys. Rev. A 21:2136 (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 Grabert et 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.

• Research Organization: Theoretical Division, University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 5746715
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 38:2; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUCTUATIONS
FOKKER-PLANCK EQUATION
IRREVERSIBLE PROCESSES
LANGEVIN EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
THERMODYNAMICS
VARIATIONS