Approach to Steady-State in Nested Resetting Processes
Abstract
We characterise the approach to nonequilibrium steady state in nested resetting processes by deriving accumulation times for the system, which quantify the effective first-passage time for the local establishment of steady state. For equal resetting rates, we obtain closed-form expressions showing that relaxation propagates as a wavefront with a delay that increases linearly along the resetting chain. We then extend this analysis to heterogeneous resetting rates, deriving exact steady-state distributions, spatial moments and accumulation times for both degenerate and non-degenerate resetting rates. We show that relaxation to steady state is ultimately governed by the minimum resetting rate in the system and, in degenerate systems, its multiplicity. These results provide a comprehensive analytical description of first-passage to nonequilibrium steady state in hierarchically coupled stochastic resetting systems, with potential applications to relaxation and transport processes in biological systems.
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BibTeX
@misc{britton2026approach,
title = {{Approach to Steady-State in Nested Resetting Processes}},
author = {Callum Britton and Ben Le Jeune and Henry Alston and Paul C. Bressloff and Thibault Bertrand},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25252},
eprint = {2609.25252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25252},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Approach to Steady-State in Nested Resetting Processes
AU - Callum Britton
AU - Ben Le Jeune
AU - Henry Alston
AU - Paul C. Bressloff
AU - Thibault Bertrand
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25252
UR - https://arxiv.org/abs/2609.25252
AB - We characterise the approach to nonequilibrium steady state in nested resetting processes by deriving accumulation times for the system, which quantify the effective first-passage time for the local establishment of steady state. For equal resetting rates, we obtain closed-form expressions showing that relaxation propagates as a wavefront with a delay that increases linearly along the resetting chain. We then extend this analysis to heterogeneous resetting rates, deriving exact steady-state distributions, spatial moments and accumulation times for both degenerate and non-degenerate resetting rates. We show that relaxation to steady state is ultimately governed by the minimum resetting rate in the system and, in degenerate systems, its multiplicity. These results provide a comprehensive analytical description of first-passage to nonequilibrium steady state in hierarchically coupled stochastic resetting systems, with potential applications to relaxation and transport processes in biological systems.
ER -