Time Dependence of Entropy Flux and Entropy Production for a Time-Delayed Dynamical System Driven by Cross-Correlated Noises

Abstract

We study the relaxation of a dissipative dynamical system with time delay and cross-correlated noises in the absence and presence of a non-equilibrium constraint in terms of the information entropy flux and production for the case of small delays. Based on the delay Fokker-Planck equation and the entropy balance equation, the time dependence of the entropy flux and entropy production of the system is derived when the delay time is small. Our calculation shows how the relaxation time depends on the delay time. We also consider how the non-equilibrium constraint is affected by the system parameters, such as the cross-correlation intensity, strength of dissipation, and delay time. The interplay among the non-equilibrium constraint, dissipation, time delay, and inter-correlated noises reveals some interesting extremal nature in the time dependence of the entropy flux and entropy production.