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Causality, time-reversal invariance and the Langevin equation

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  • Mazur, P.
  • Bedeaux, D.

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.

Suggested Citation

  • Mazur, P. & Bedeaux, D., 1991. "Causality, time-reversal invariance and the Langevin equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 155-174.
    • Handle: RePEc:eee:phsmap:v:173:y:1991:i:1:p:155-174
    DOI: 10.1016/0378-4371(91)90256-C
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