Shear-Driven Diffusion with Stochastic Resetting

TL;DR

This paper investigates the non-equilibrium behavior of particles under shear flow and stochastic resetting, revealing a crossover from diffusive to super-diffusive regimes and complex skewness behavior.

Contribution

It introduces a perturbative approach to derive the steady-state distribution considering shear-induced anisotropy and explores the effects of resetting on particle dynamics.

Findings

Crossover from diffusive to super-diffusive regimes due to shear.

Non-monotonic skewness behavior across regimes.

Resetting incurs energetic costs and affects steady-state existence.

Abstract

External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and stochastic resetting. The particle diffuses with a constant diffusion coefficient while simultaneously experiencing linear shear and being stochastically returned to its initial position at a constant rate. We perturbatively derive the steady-state probability distribution that captures the effects of shear-induced anisotropy on the spatial structure of the distribution. We show that the dynamics perform a crossover from a diffusive to a super-diffusive regime, which cease to exist in the absence of shear flow. We also show that the skewness has a non-monotonic behavior when one passes from the shear-dominated to the resetting-dominated regime. We demonstrate that at small resetting rates, while resetting events are rare, they incur a large energetic cost to sustain the non-equilibrium steady state. Surprisingly, if only the $x$-position is reset, the system never reaches a steady state but instead spreads diffusively.