Shear-Driven Diffusion with Stochastic Resetting
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914971570405376 |
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| author | Abdoli, Iman Olsen, Kristian Stølevik Löwen, Hartmut |
| author_facet | Abdoli, Iman Olsen, Kristian Stølevik Löwen, Hartmut |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shear-Driven Diffusion with Stochastic Resetting Abdoli, Iman Olsen, Kristian Stølevik Löwen, Hartmut Statistical Mechanics Soft Condensed Matter 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. |
| title | Shear-Driven Diffusion with Stochastic Resetting |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2410.10333 |