Irreversibility in linear systems with colored noise

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.

11 pages, 4 figures

References in corpus (9)

• Self-motile colloidal particles: from directed propulsion to random walk
• Non-equilibrium mechanics and dynamics of motor activated gels
• Non-equilibrium microtubule fluctuations in a model cytoskeleton
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Time-(ir)reversibility in active matter: from micro to macro
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Fluctuation Properties of Steady-State Langevin Systems
• Nonequilibrium oscillations, probability angular momentum, and the climate system
• Scaling behavior of non-equilibrium measures in internally driven elastic assemblies