Heat flow due to time-delayed feedback

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.