Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models

TL;DR

This paper demonstrates that in driven non-equilibrium Langevin systems, Gaussian noise and time-reversal symmetry are equivalent, leading to restrictions on probability distributions, validated through polymer and Brownian particle models.

Contribution

It establishes the equivalence of Gaussian noise and time-reversal symmetry in driven Langevin systems and explores their implications on probability distributions.

Findings

Gaussian noise and time-reversal symmetry are equivalent in driven systems

External force potential condition restricts probability distribution forms

Validated results with polymer stretching and Brownian suspension models

Abstract

We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of non-interacting Brownian particles in steady flow.