Fluctuations of macrovariables in nonlinear systems: Langevin equation approach

Abstract

Fluctuations in nonlinear Markovian systems are studied by the Langevin equation method using system-size expansion. Langevin equations with different random sources are constructed for the description of fluctuations to varying degrees of accuracy in inverse powers of the system size ε Evolution equations for the deterministic path, deviation of the mean from the deterministic path, and the variance are obtained in a nonstationary state in the lowest order of ε . The power spectral density for fluctuations about a stable equilibrium is calculated correct to order ε 2 and is compared to the exact expression for the Alkemade diode. The relaxation frequency for the decay of correlations in a critical equilibrium and the scaling law for the anomalous fluctuations are determined and compared to those obtained by Kubo et al .