  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.
