The induced motion of a probe coupled to a bath with random resettings

Abstract

We consider a probe linearly coupled to the center of mass of a nonequilibrium bath. We study the induced motion on the probe for a model where a resetting mechanism is added to an overdamped bath dynamics with quadratic potentials. The fact that each bath-particle is at random times being reset to a fixed position is known for optimizing diffusive search strategies, but here stands for the nonequilibrium aspect of the bath. In the large bath scaling limit the probe is governed by an effective Langevin equation. Depending on the value of the parameters, there appear three regimes: (i) an equilibrium-like regime but with a reduced friction and an increased effective temperature; (ii) a regime where the noise felt by the probe is continuous but nonGaussian and exhibits fat-tails; (iii) a regime with a nonGaussian noise exhibiting power-law distributed jumps. The model thus represents an exactly solvable case for the origin of nonequilibrium probe dynamics.

17 pages, 4 figures; v2: refs updated, published version

References in corpus (4)

• Diffusion in a potential landscape with stochastic resetting
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• On the generalized Langevin equation for a Rouse bead in a nonequilibrium bath
• How statistical forces depend on thermodynamics and kinetics of driven media

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• Controlling particle currents with evaporation and resetting from an interval
• Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems
• Violation of the second fluctuation-dissipation relation and entropy production in nonequilibrium medium
• Conditioned backward and forward times of diffusion with stochastic resetting: a renewal theory approach
• Stationary state of harmonic chains driven by boundary resetting
• Stabilization in the eye of a cyclone