The Langevin equation for systems with a preferred spatial direction

TL;DR

This paper extends the Langevin equation to systems with a preferred spatial direction caused by external forces, enabling prediction of fluctuation properties in both equilibrium and nonequilibrium steady states.

Contribution

It introduces a generalized Langevin equation incorporating bias from external forces, expanding the theoretical framework for asymmetric systems.

Findings

Derived a modified Langevin equation with bias term

Predicted fluctuation statistics from physical observables

Applicable to both equilibrium and nonequilibrium steady states

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.