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

## TL;DR

This paper analyzes the dynamics of a probe coupled to a nonequilibrium bath with random resettings, revealing three distinct regimes of motion characterized by effective temperature, non-Gaussian noise, and power-law jumps.

## Contribution

It introduces an exactly solvable model of probe dynamics in a nonequilibrium bath with resetting, identifying three distinct dynamical regimes.

## Key findings

- Identification of equilibrium-like regime with reduced friction and increased temperature
- Discovery of a non-Gaussian noise regime with fat tails
- Observation of a regime with power-law distributed jumps

## 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.