Irreversibility, heat and information flows induced by non-reciprocal interactions

Abstract

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general 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 renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear 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 flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous ‘Maxwell demon’. We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay

“…To this end, we utilize and extend results from Ref. [57], where we have explored the connection between coupling topology A and the thermodynamic properties for generic linear systems of the type (5). We note that more general coupling topologies also allow to model other physical systems, as active particles [57].…”

“…In the case T = 0, this embedding is called the "linear chain trick" [31,62]. The asymmetry of the coupling matrix A is associated with nonreciprocal interactions between the X j [57]. Further, if the external potential in Equation ( 2) is parabolic, φ = 0, otherwise φ = [aX 0 − V ] (1 0 .…”

“…Interestingly and contrary to the delay distribution K, which dramatically changes between n = 1 and n = 2, the correlations of the colored noise (Equation ( 6)) remain very similar for all n. They decay monotonically in all cases (see Figure 2). Indeed, as we have explicitly shown in [57], the system with colored noise (Equation ( 6)) and delay distribution (Equation ( 3)) never fulfills the fluctuation-dissipation relation (FDR) of second kind, indicating the inherent non-equilibrium nature of the non-Markovian process X 0 (Equation ( 2 )). An exception is the case n = 1 with…”

“…where FDR is fulfilled. As we have discussed in [57], a way to understand the broken FDR are the involved non-reciprocal, interactions in the corresponding Markovian representation (Equation ( 5)). We have further shown in [57] that the detailed balance (DB) condition is as well only fulfilled for n = 1 and condition (Equation ( 7)).…”

“…For example, a delay force acting on a colloid can induce a net heat flow from the heat bath to the colloid, i.e., a reduction of the medium entropy [43,50]. This refrigeration effect, called feedback cooling, is closely related to feedback cooling and "entropy pumping" in Markovian inertial systems with velocitydependent feedback [51][52][53][54][55][56] (specifically, the delay force has a comparable effect as a velocity-dependent force, and both induce entropy pumping, see [43,57]). While these effects are, in principle, known, we are still only at the beginning of a full understanding of the impact of delay on stochastic dynamics.…”