Non-Markovian escape under stochastic resetting

Debasish Saha; Rati Sharma

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arXiv · 2509.11608

Non-Markovian escape under stochastic resetting

Debasish Saha·Rati Sharma

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Abstract

Stochastic resetting is a powerful strategy known to optimize target-search processes at microscopic scales. While its effects on Markovian systems are well understood, its influence on memory-driven systems, such as in viscoelastic baths, has not been adequately investigated. In this work, we study the first-passage properties of escape for a harmonically trapped particle in a non-Markovian environment under stochastic resetting. We employ a complete renewal approach and find that the characteristic non-exponential heavy tail of the first-passage time (FPT) distribution becomes exponential when resetting is introduced. We further find that optimal resetting is achievable at a lower reset rate when the dynamics are weakly correlated; however, for stronger correlations, the process needs to be reset more frequently. Therefore, resetting in memory-driven dynamics can be used as an effective control strategy to initiate faster escape, thereby regulating efficient transport mechanisms in complex chemical and biomolecular environments that follow non-Markovian dynamics.

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Debasish Saha, Rati Sharma. 2025-09-15. Non-Markovian escape under stochastic resetting. https://arxiv.org/abs/2509.11608

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