The transition to collective motion in nonreciprocal active matter: coarse graining agent-based models into fluctuating hydrodynamics

Two hallmarks of non-equilibrium systems, from active colloids to animal herds, are agents motility and nonreciprocal interactions. Their interplay creates feedback loops leading to complex spatiotemporal dynamics which are crucial to understand the non-linear response of active systems. To study such response, we introduce a minimal model featuring both motility and nonreciprocity at the microscopic scale while admitting an exact hydrodynamic theory valid also in the nonlinear regime. This rigorous coarse-graining, complemented by numerical simulations, allows us to quantitatively assess the hitherto neglected impact of inter-species nonreciprocity on a paradigmatic transition in active matter: the emergence of collective motion. When nonreciprocity is weak, we show that flocking is accelerated and bands tend to synchronize with a spatial overlap controlled by nonlinearities. When nonreciprocity is strong, flocking is superseded by a Chase & Rest dynamical phase where each species alternates between a chasing state, when they propagate, and a resting state, when they stand still. Finally, we demonstrate how fluctuations in finite systems can be harnessed to characterize microscopic non-reciprocity from macroscopic time-correlation functions, even in phases where nonreciprocal interactions do not affect the thermodynamic steady-state.