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We show that memory, feedback, and activity are all describable by the sameunifying concept, that is non-reciprocal (NR) coupling. We demonstrate thatcharacteristic thermodynamic features of these intrinsically nonequilibriumsystems are reproduced by low-dimensional Markovian networks with NR coupling,which we establish as minimal models for such complex systems. NR couplingalone implies a violation of the fluctuation-dissipation relation, which isinevitably connected to entropy production, i.e., irreversibility. Hiding theNR coupled degrees of freedom renders non-Markovian, one-variable Langevindescriptions with complex types of memory, for which we find a generalizedsecond law involving information flow. We demonstrate that non-monotonic memoryis inextricably linked to NR coupling. Furthermore, we discuss discrete timedelay as the infinite-dimensional limit, and find a divergent entropyproduction, corresponding to unbounded cost for precisely storing a Browniantrajectory.

Non-reciprocal hidden degrees of freedom: A unifying perspective on memory, feedback, and activity