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    Target Search Optimization by Threshold Resetting

    Arup Biswas1,2,*, Satya N. Majumdar3,†, and Arnab Pal1,2,‡

    • *Contact author: arupb@imsc.res.in
    • †Contact author: satyanarayan.majumdar@cnrs.fr
    • ‡Contact author: arnabpal@imsc.res.in

    Phys. Rev. Lett. 135, 227101 – Published 24 November, 2025

    DOI: https://doi.org/10.1103/752c-wqly

    Abstract

    We introduce a new class of first-passage time optimization driven by threshold resetting, inspired by many natural processes where crossing a critical limit triggers failure, degradation, or transition. Here, search agents are collectively reset when a threshold is reached, creating event-driven, system-coupled simultaneous resets that induce long-range interactions. We develop a unified framework to compute mean search times for these correlated stochastic processes, with ballistic and diffusive searchers as key examples uncovering diverse optimization behaviors. A cost function, akin to breakdown penalties, reveals that optimal resetting can forestall larger losses. This formalism generalizes to broader stochastic systems with multiple degrees of freedom.

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