Non-reciprocity across scales in physical, biological, and social systems

From cellular oscillations to human migration, the living world is teeming with macroscopic activity driven by non-reciprocal interactions that are asymmetric and therefore unable to be derived from an optimization principle. While it is well known that non-reciprocity breaks time-reversal symmetry, its impact on spatial patterns is unclear.In this talk, I give an overview of the macroscopic fate of microscopic non-reciprocity in spatially-extended systems.I will begin by discussing the fate of oscillatory states in non-reciprocal spin systems, where we will see that spatial coupling and noise can defy mean-field expectations. Such oscillations can guide biological function and necessarily cost energy, but analysis of experiments on the excitable cell cortex shows that energetic costliness does not always correlate with biological function. This disconnection between dynamics and function also emerges in human social systems, where asymmetric social preferences lead to the emergence of memory with impacts on racial (de)segregation in continuum models of human residential dynamics.Taken together, these results show the often counter-intuitive way that non-equilibrium activity can manifest in large-scale patterns, with multi-disciplinary implications from statistical mechanics to urban planning.