Heat flow due to time-delayed feedback

TL;DR

This paper develops an analytical method to quantify steady-state heat flow in nonlinear overdamped systems with time-delayed feedback, revealing feedback-induced heating, cooling, and entropy production phenomena.

Contribution

It introduces a novel analytical approach to analyze heat flux in non-Markovian systems with time delay, expanding understanding of thermodynamics in such systems.

Findings

Feedback causes finite heat flow even at very small delays.

Feedback can induce both heating and cooling regimes.

Maximum entropy production occurs at coherence resonance conditions.

Abstract

The thermodynamics of stochastic non-Markovian systems is still widely unexplored. We present an analytical approach for the net steady-state heat flux in nonlinear overdamped systems subject to a continuous feedback force with a discrete time delay. We show that the feedback inevitably leads to a finite heat flow even for vanishingly small delay times. Application to an exemplary (bistable) system reveals that the feedback induces heating as well as cooling regimes and leads to a maximum of the medium entropy production at coherence resonance conditions.