Description:
We study the thermodynamic properties induced by non-reciprocal interactions betweenstochastic degrees of freedom in time- and space-continuous systems. We show that, under fairlygeneral conditions, non-reciprocal coupling alone implies a steady energy flow through the system,i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom rendersnon-Markovian, one-variable Langevin descriptions with complex types of memory, for which wefind a generalized second law involving information flow.We demonstrate that non-reciprocallinear interactions can be used to engineer non-monotonic memory, which is typical for, e.g.,time-delayed feedback control, and is automatically accompanied with a nonzero information flowthrough the system. Furthermore, already a single non-reciprocally coupled degree of freedom canextract energy from a single heat bath (at isothermal conditions), and can thus be viewed as aminimal version of a time-continuous, autonomous ‘Maxwell demon’.We also show that forappropriate parameter settings, the non-reciprocal system has characteristic features of activematter, such as a positive energy input on the level of the fluctuating trajectories without globalparticle transport.