Entropy production of nonreciprocal interactions

Nonreciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we introduce a nonmotile active particle system where activity originates from asymmetric, pairwise interaction forces that result in an injection of energy at the microscopic scale. We calculate stationary correlation functions and entropy production rate in three exactly solvable cases, and analyze a more general case in a perturbation theory as an expansion in weak interactions. Our results show that equilibrium may be recovered by adjusting the diffusion constants despite nonreciprocity, revealing an equivalence in the absolute amplitude of the force and diffusivity. We support our analytical results with numerical simulations.