While all fundamental physical interactions obey the law of action-equals-reaction, the dynamics we effectively observe in complex nonequilibrium systems ubiquitously break reciprocity at different scales. In this talk, I will discuss the intricate connection between nonreciprocity and time-reversal symmetry breaking, and how irreversibility in nonreciprocal systems manifests itself in terms of thermodynamic properties as well as emergent collective behavior. I will first show that even for a simple system of two Brownian particles, nonreciprocity can have surprising thermodynamic implications, such as the generation of heat flows against a temperature gradient which can be related to the information exchange through the coupling [1]. I will then discuss the collective behavior in nonreciprocal systems. For binary fluid mixtures, we find that fluctuations near nonreciprocal phase transitions, fluctuations not only inflate, as in equilibrium criticality, but also develop an asymptotically increasing time-reversal asymmetry and associated surge entropy production [2,3]. Introducing nonreciprocal coupling in the XY model, we show how nonreciprocity can lead to the formation of true long-range order in two dimensions [4], but can also induce spatiotemporal chaos that can be regarded as self-generated noise.

[1] Loos and Klapp, NJP 22, 123051 (2020).
[2] Suchanek, Kroy, and Loos, PRL 131, 258302 (2023).
[3] Suchanek, Kroy, and Loos, PRE 108, 064610 (2023), PRE 108, 064123 (2023).
[4] Loos, Klapp, Martynec, Phys. Rev. Lett. 130, 198301 (2023).