Breakdown of Linear Response Induced by Velocity-Dependent Stochastic Resetting

TL;DR

This paper demonstrates that linear response theory can break down in nonequilibrium systems with velocity-dependent stochastic resetting, leading to nonlinear transport behavior in a minimal model.

Contribution

It introduces a solvable model showing how velocity-dependent resetting causes nonlinear response, challenging the universality of linear response theory.

Findings

Exact steady-state velocity distribution derived

Mean velocity follows a power law with external force

Velocity-dependent resetting induces nonlinear transport

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 driven Langevin particle subject to a resetting mechanism whose rate grows as a power of the particle velocity, motivated by transport processes where faster carriers experience more frequent scattering events. 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 particular, the mean velocity obeys the exact power law $\langle v\rangle \propto F^{1/(\alpha+1)}$, where $\alpha$ characterizes the velocity dependence of the resetting rate. 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.