Breakdown of linear response induced by velocity-dependent stochastic resetting

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Abstract
Linear response theory lies at the foundation of transport phenomena, predicting that physical systems respond proportionally to weak external forces. Here, we show that this principle can break down in a minimal nonequilibrium setting due to state-dependent stochastic resetting. We consider a Langevin particle driven by a constant external force F and subject to a velocity-dependent resetting rate r(v)=λ|v|^{α}, where α controls the velocity dependence of the resetting. We derive the exact steady-state velocity distribution and establish a moment balance relation that links external driving, viscous dissipation, and resetting-induced dissipation. This relation reveals that the response is controlled by a nonlinear coupling between the velocity and the resetting rate, leading to nonlinear transport. In the deterministic limit without friction and diffusion, the mean velocity obeys the exact power law 〈v〉∝F^{1/(α+1)} at all force strengths. In the presence of friction or velocity diffusion with α>0, linear response is recovered at weak driving, followed by a crossover to the same nonlinear scaling at strong driving. Our results provide a solvable example in which linear response fails at the level of the leading-order behavior and identify velocity-dependent resetting as a minimal dynamical mechanism for generating nonlinear transport in nonequilibrium steady states. More broadly, they suggest a framework for understanding transport in stochastic systems with feedback or environment-dependent dynamics.
Funding Information
  • Japan Society for the Promotion of Science (21K03392)

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