Non-monotonic diffusion from nonequilibrium driving

The stochastic dynamics of interacting particles far from equilibrium remains a fundamental challenge in statistical physics. While reciprocal interactions often permit effective one-body descriptions, such reductions generally fail for nonreciprocal interactions, which are ubiquitous in driven and active systems. We develop a unified theoretical framework for interacting particles with reciprocal and nonreciprocal couplings, applicable to the principal classes of active matter, including run-and-tumble, active Brownian, and active Ornstein-Uhlenbeck particles. As a minimal example, we study a passive particle driven by an active particle. On a periodic ring, we show analytically that the driven particle is always diffusive at long times, independent of the microscopic driving mechanism. Analytical predictions and numerical simulations reveal a nonmonotonic dependence of the effective diffusivity on the driving activity, giving rise to both enhanced and suppressed transport. Remarkably, the same behavior occurs in an equilibrium system driven out of equilibrium by coupling the driving particle to a higher local temperature. Our framework quantitatively captures both systems, identifies the common mechanism underlying the nonmonotonic transport, and establishes a unified description of transport under active and passive nonequilibrium driving.