Emergence of hidden nonreciprocity as a stabilizing effective potential in active matter

Nonreciprocal interactions are ubiquitous, ranging from colloidal particles to neurons to social dynamics. These nonconservative forces are known to induce complex oscillations between different states. Here, we identify a special class of systems evolving on a potential and under nonreciprocal interactions. These models are distinguished by their stationary and exactly solvable steady-state distributions of positions. Under thermal noise, an equilibrium Boltzmann distribution characterizes the steady state, showing no sign of nonreciprocity. Under exponentially correlated noise, which is characteristic of active matter, the nonreciprocity emerges in the steady-state distribution as an effective potential that stabilizes minima of the true potential. Thus, we reveal an unexpected interplay involving active fluctuations and reciprocal and nonreciprocal couplings. Our findings have interesting implications for the role and detection of nonreciprocity.