The Langevin equation for systems with a preferred spatial direction

Abstract

In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients.

1 figure

References in corpus (3)

• Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise
• Asymptotic derivation of Langevin-like equation with non-Gaussian noise and its analytical solution
• Asymmetry of steady state current fluctuations in nonequilibrium systems

Cited by in corpus (6)

• Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics
• Poissonian cellular Potts models reveal nonequilibrium kinetics of cell sorting
• Second-order fluctuation theory and time autocorrelation function for currents
• Effective temperatures for single particle system under dichotomous noise
• Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid
• Jump Processes with Deterministic and Stochastic Controls