Hidden nonreciprocity as a stabilizing effective potential in active matter

Matthew Du, Suriyanarayanan Vaikuntanathan

Published 2024-01-26Version 1

Active matter with nonreciprocal interactions is known for its distinctive dynamics. To shed light on the stationary properties of such systems, we consider paradigmatic systems of nonreciprocally coupled active Ornstein-Uhlenbeck particles. For each system, we uniquely decompose the interparticle force into an energy gradient and a transverse nonconservative force. We show that the steady-state distribution of positions, which would only reflect the energy if the noise were thermal, features the transverse force as an effective potential that stabilizes the energy minima, due to the persistent noise that propels the particles. We exactly solve the distribution for nonreciprocal harmonic oscillators and numerically verify the effective stability for systems with more complex couplings. Our work suggests that energy injection at the single-particle level controls how, if at all, nonreciprocity in the interactions appears in stationary states of active matter.