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  • Open Access

Universal linear response of first-passage kinetics: A framework for prediction and inference

Tommer D. Keidar and Shlomi Reuveni*

  • School of Chemistry, The Center for Computational Molecular and Materials Science, The Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv, Israel

  • *Contact author: shlomire@tauex.tau.ac.il
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Phys. Rev. Research 8, 023135 – Published 7 May, 2026

DOI: https://doi.org/10.1103/c7wy-ddrc

Abstract

First-passage processes are pervasive across numerous scientific fields, yet a general framework for understanding their response to external perturbations remains elusive. While the fluctuation-dissipation theorem offers a complete linear response theory for systems in steady state, it fails to apply to transient first-passage processes. We address this challenge by focusing on rare—rather than weak—perturbations. Surprisingly, we discover that the linear response of the mean first-passage time (MFPT) to such perturbations is universal. It depends solely on the first two moments of the unperturbed first-passage time and the mean completion time following perturbation activation, without any assumptions about the underlying system's dynamics. To demonstrate the utility of our findings, we analyze the MFPT response of drift-diffusion processes in two scenarios: (1) stochastic resetting with information feedback and (2) an abrupt transition from a linear to a logarithmic potential. In both cases, our approach bypasses the need for explicit determination of the perturbed dynamics, unraveling a highly nontrivial response landscape with minimal effort. Finally, we show how our framework enables a new type of experiment—inferring molecular-level fluctuations from bulk measurements, a feat previously believed to be impossible. Overall, the universality reported herein offers a powerful tool for predicting the impact of perturbations on kinetic processes—and, remarkably, for extracting hidden single-molecule fluctuations from accessible bulk measurements.

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Phys. Rev. Research 8, 023135– Published 7 May, 2026
  • Received 5 August 2025
  • Accepted 6 April 2026
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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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