Augmented langevin description of multiplicative noise and nonlinear dissipation in Hamiltonian systems

Journal Article · Wed Oct 01 04:00:00 EDT 1986 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01033092· OSTI ID:6918093

Ramshaw, J D; Lindenberg, K

The augmented Langevin approach described in a previous article is applied to the problem of introducing multiplicative noise and nonlinear dissipation into an arbitrary Hamiltonian system in a thermodynamically consistent way, so that a canonical equilibrium distribution is approached asymptotically at long times. This approach leads to a general nonlinear fluctuation-dissipation relation which, for a given form of the multiplicative noise (chosen on physical grounds), uniquely determines the form of the nonlinear dissipative terms needed to balance the fluctuations. In addition to the noise and dissipation terms, the augmented Langevin equation contains an addition term whose form depends on the stochastic interpretation rule used. This term vanishes when the stratonovich rule is chosen and the noise itself is of a Hamiltonian origin. This development provides a simple phenomenological route to results previously obtained by detailed analysis of microscopic system-bath models. The procedure is illustrated by applications to a mechanical oscillator with fluctuating frequency, a classical spin in a fluctuating magnetic field, and the Brownian motion of a rigid rotor.

• Research Organization: Los Alamos National Lab., NM
• OSTI ID: 6918093
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 45:1/2; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
BROWNIAN MOVEMENT
DIFFERENTIAL EQUATIONS
DISSIPATION FACTOR
DYNAMICS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUATIONS OF MOTION
EQUIPMENT
FOKKER-PLANCK EQUATION
HARMONIC OSCILLATORS
LANGEVIN EQUATION
MAGNETIC FIELDS
MATHEMATICAL MODELS
MECHANICS
NOISE
NONLINEAR PROBLEMS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
ROTORS
SPIN
THERMODYNAMICS