Causality, time-reversal invariance and the Langevin equation

P. Mazur and D. Bedeaux

Physica A: Statistical Mechanics and its Applications, 1991, vol. 173, issue 1, 155-174

Abstract: It is shown that the assumptions of causality and time-reversal invariance severely restrict the possibility to describe the fluctuations of a variable in a nonlinear Markovian system using a Langevin equation. In fact a theorem is proven which implies that a Langevin force which is independent of the state of the system is necessarily Gaussian and white. The theorem furthermore implies that such a description is only possible if the so-called “systematic force” is proportional to the derivative of the logarithm of the equilibrium distribution of the variable. Our analysis is given for a system with one variable, which may be either even or odd under time reversal.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:173:y:1991:i:1:p:155-174

DOI: 10.1016/0378-4371(91)90256-C

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