Non-equilibrium dynamics of drift-diffusion process under threshold resetting
Abstract
We study the emergence of non-equilibrium steady states (NESS) in stochastic processes under threshold resetting, an event-driven protocol in which the system resets to its initial configuration upon crossing a prescribed spatial boundary (threshold). In contrast to externally driven resetting, whose steady-state properties are well understood, the behavior under threshold resetting remains largely unexplored. We derive general conditions for the existence of a NESS and show that, whenever it exists, the steady state at a given position x can be expressed as the ratio of two fundamental quantities: the mean local time (MLT) at x and the mean first-passage time (MFPT) to hit the threshold. In particular, for noisy systems, a finite MFPT guarantees the existence of a NESS. As an illustrative example, we analyze a drift-diffusion process in one dimension and uncover rich intermediate-time dynamics, including anomalous relaxation in the spatial distribution, damped oscillations in the moments and in the mean-squared displacement (MSD), governed by system parameters. Our findings provide a general understanding of the emergence of non-equilibrium steady states and relaxation dynamics under threshold resetting, revealing how induced events shape the spatial and temporal properties of a broad class of stochastic processes.
Related
- Slow-fast dynamics of the McKean model with stochastic resetting and diffusion
- Multi-Energy Analysis of Baryon Stopping: Extracting Non-Equilibrium Dynamics via Stochastic Rapidity Diffusion
- Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting
- Diffusion with stochastic resetting in the presence of a delta killing trap: Drift-controlled survival regimes
- Equilibrium fluctuations of the weakly asymmetric inclusion process
BibTeX
@misc{das2026nonequilibrium,
title = {{Non-equilibrium dynamics of drift-diffusion process under threshold resetting}},
author = {Rahul Das and Satya N Majumdar and Arnab Pal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24438},
eprint = {2609.24438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24438},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-equilibrium dynamics of drift-diffusion process under threshold resetting
AU - Rahul Das
AU - Satya N Majumdar
AU - Arnab Pal
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24438
UR - https://arxiv.org/abs/2609.24438
AB - We study the emergence of non-equilibrium steady states (NESS) in stochastic processes under threshold resetting, an event-driven protocol in which the system resets to its initial configuration upon crossing a prescribed spatial boundary (threshold). In contrast to externally driven resetting, whose steady-state properties are well understood, the behavior under threshold resetting remains largely unexplored. We derive general conditions for the existence of a NESS and show that, whenever it exists, the steady state at a given position x can be expressed as the ratio of two fundamental quantities: the mean local time (MLT) at x and the mean first-passage time (MFPT) to hit the threshold. In particular, for noisy systems, a finite MFPT guarantees the existence of a NESS. As an illustrative example, we analyze a drift-diffusion process in one dimension and uncover rich intermediate-time dynamics, including anomalous relaxation in the spatial distribution, damped oscillations in the moments and in the mean-squared displacement (MSD), governed by system parameters. Our findings provide a general understanding of the emergence of non-equilibrium steady states and relaxation dynamics under threshold resetting, revealing how induced events shape the spatial and temporal properties of a broad class of stochastic processes.
ER -