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  • Open Access

Nested Stochastic Resetting: Nonequilibrium Steady States and Exact Correlations

Henry Alston*, Callum Britton*, and Thibault Bertrand†

  • *These authors contributed equally to this work.
  • †Contact author: t.bertrand@imperial.ac.uk
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Phys. Rev. Lett. 135, 167101 – Published 15 October, 2025

DOI: https://doi.org/10.1103/ccjj-6ksn

Abstract

Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states. Here, we consider a chain of diffusive processes xi(t) that interact unilaterally: at random time intervals, the process xn stochastically resets to the instantaneous value of xn−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 ⟨xnxn+j⟩ 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 modeling of lossy information propagation.

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Phys. Rev. Lett. 135, 167101– Published 15 October, 2025
  • Received 27 January 2025
  • Accepted 10 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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