Age-structured hydrodynamics of ensembles of anomalously diffusing particles with renewal resetting
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| Format: | Preprint |
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2025
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| _version_ | 1866915969516961792 |
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| author | Meerson, Baruch Vilk, Ohad |
| author_facet | Meerson, Baruch Vilk, Ohad |
| contents | We develop an age-structured hydrodynamic (HD) theory which describes the collective behavior of $N\gg 1$ anomalously diffusing particles under stochastic renewal resetting. The theory treats the age of a particle -- the time since its last reset -- as an explicit dynamical variable and allows for resetting rules which introduce global inter-particle correlations. The anomalous diffusion is modeled by the scaled Brownian motion (sBm): a Gaussian process with independent increments, characterized by a power-law time dependence of the diffusion coefficient, $D(t)\sim t^{2H-1}$, where $H>0$. We apply this theory to three different resetting protocols: independent resetting to the origin (model~A), resetting to the origin of the particle farthest from it (model~B), and a scaled-diffusion extension of the ``Brownian bees" model of Berestycki et al, Ann. Probab. \textbf{50}, 2133 (2022). In all these models non-equilibrium steady states are reached at long times, and we determine the steady-state densities. For model A the (normalized to unity) steady-state density coincides with the steady-state probability density of a single particle undergoing sBM with resetting to the origin. For model B, and for the scaled Brownian bees, the HD steady-state densities are markedly different: in particular, they have compact supports for all $H>0$. The age-structured HD formalism can be extended to other anomalous diffusion processes with renewal resetting protocols which introduce global inter-particle correlations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Age-structured hydrodynamics of ensembles of anomalously diffusing particles with renewal resetting Meerson, Baruch Vilk, Ohad Statistical Mechanics Mathematical Physics We develop an age-structured hydrodynamic (HD) theory which describes the collective behavior of $N\gg 1$ anomalously diffusing particles under stochastic renewal resetting. The theory treats the age of a particle -- the time since its last reset -- as an explicit dynamical variable and allows for resetting rules which introduce global inter-particle correlations. The anomalous diffusion is modeled by the scaled Brownian motion (sBm): a Gaussian process with independent increments, characterized by a power-law time dependence of the diffusion coefficient, $D(t)\sim t^{2H-1}$, where $H>0$. We apply this theory to three different resetting protocols: independent resetting to the origin (model~A), resetting to the origin of the particle farthest from it (model~B), and a scaled-diffusion extension of the ``Brownian bees" model of Berestycki et al, Ann. Probab. \textbf{50}, 2133 (2022). In all these models non-equilibrium steady states are reached at long times, and we determine the steady-state densities. For model A the (normalized to unity) steady-state density coincides with the steady-state probability density of a single particle undergoing sBM with resetting to the origin. For model B, and for the scaled Brownian bees, the HD steady-state densities are markedly different: in particular, they have compact supports for all $H>0$. The age-structured HD formalism can be extended to other anomalous diffusion processes with renewal resetting protocols which introduce global inter-particle correlations. |
| title | Age-structured hydrodynamics of ensembles of anomalously diffusing particles with renewal resetting |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2512.14345 |