Stochastic resetting in a nonequilibrium environment

TL;DR

This paper investigates how stochastic resetting affects a tracer particle's dynamics in a nonequilibrium medium with memory effects, revealing how bath particle diffusivities influence search efficiency and relaxation.

Contribution

It introduces a framework for analyzing resetting in non-Markovian systems with memory effects, highlighting the role of bath particle diffusivities and external forces.

Findings

Coupling to hot bath particles accelerates search times.

Coupling to cold bath particles hinders the search process.

External forces modulate the interplay between coupling strength and diffusivity.

Abstract

This study examines the dynamics of a tracer particle diffusing in a nonequilibrium medium under stochastic resetting. The nonequilibrium state is induced by harmonic coupling between the tracer and bath particles, generating memory effects with exponential decay in time. We explore the tracer's behavior under a Poissonian resetting protocol, where resetting does not disturb the bath environment, with a focus on key dynamical behavior and first-passage properties, both in the presence and absence of an external force. The interplay between coupling strength and diffusivity of bath particle significantly impacts both the tracer's relaxation dynamics and search time, with external forces further modulating these effects. Our analysis identifies distinct hot and cold bath particles based on their diffusivities, revealing that coupling to a hot particle facilitates the searching process, whereas coupling to a cold particle hinders it. Using a combination of numerical simulations and analytical methods, this study provides a comprehensive framework for understanding resetting mechanisms in non-Markovian systems, with potential applications to complex environments such as active and viscoelastic media, where memory-driven dynamics and nonequilibrium interactions are significant.