Nested Stochastic Resetting: Nonequilibrium Steady-states and Exact Correlations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929699069886464 |
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| author | Alston, Henry Britton, Callum Bertrand, Thibault |
| author_facet | Alston, Henry Britton, Callum Bertrand, Thibault |
| contents | Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$ stochastically resets to the instantaneous value of $x_{n-1}$. We derive analytically the steady-state statistics of these nested stochastic resetting processes including the stationary distribution for each process as well as its moments. We are also able to calculate exactly the steady-state two-point correlations $\langle x_n x_{n+j}\rangle$ between processes by mapping the problem to one of the ordering statistics of random counting processes. Understanding statistics and correlations in many-particle nonequilibrium systems remains a formidable challenge and our results provide an example of such tractable correlations. We expect this framework will both help build a model-independent framework for random processes with unilateral interactions and find immediate applications, e.g. in the modelling of lossy information propagation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nested Stochastic Resetting: Nonequilibrium Steady-states and Exact Correlations Alston, Henry Britton, Callum Bertrand, Thibault Statistical Mechanics Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$ stochastically resets to the instantaneous value of $x_{n-1}$. We derive analytically the steady-state statistics of these nested stochastic resetting processes including the stationary distribution for each process as well as its moments. We are also able to calculate exactly the steady-state two-point correlations $\langle x_n x_{n+j}\rangle$ between processes by mapping the problem to one of the ordering statistics of random counting processes. Understanding statistics and correlations in many-particle nonequilibrium systems remains a formidable challenge and our results provide an example of such tractable correlations. We expect this framework will both help build a model-independent framework for random processes with unilateral interactions and find immediate applications, e.g. in the modelling of lossy information propagation. |
| title | Nested Stochastic Resetting: Nonequilibrium Steady-states and Exact Correlations |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2502.03225 |