Irreversibility in linear systems with colored noise

TL;DR

This paper investigates how temporal correlations in noise, or colored noise, influence measures of irreversibility in linear systems, extending the white noise framework to more realistic scenarios with long-lived noise correlations.

Contribution

It generalizes the theoretical framework for irreversibility measures from white noise to colored noise in linear systems, using Lyapunov equations.

Findings

Derived expressions for irreversibility measures with colored noise

Connected colored noise results to white noise limits

Provided a unified approach for analyzing non-equilibrium dynamics

Abstract

Time-irreversibility is a distinctive feature of non-equilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical noise is often approximated as white, in many real applications the time correlations of the random forces can actually be significantly long-lived compared to the relaxation times of the driven system. We analyze the effects of temporal correlations in the noise on commonly used measures of irreversibility and demonstrate how the theoretical framework for white noise driven systems naturally generalizes to the case of colored noise. Specifically, we express the auto-correlation function, the area enclosing rates, and mean phase space velocity in terms of solutions of a Lyapunov equation and in terms of their white noise limit values.