PHENOMENOLOGICAL APPROACH TO NONLINEAR LANGEVIN-EQUATIONS

In this paper we address the problem of consistently constructing Lang evin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we pro ve that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random fo rce. If the cause of the fluctuations is weakly coupled to the fluctua ting variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, micro scopic reversibility and weak coupling impose symmetry relations on th e variable-dependent Onsager coefficients. We then analyze the fluctua tions in two cases: Brownian motion in position space and an asymmetri c diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equat ion proposed here, the phenomenological theory is in agreement with th e results predicted by more microscopic models.