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  • Letter
  • Open Access

Inference from gated first-passage times

Aanjaneya Kumar1,*, Yuval Scher2,†, Shlomi Reuveni2,‡, and M. S. Santhanam1,§

  • 1Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
  • 2School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel

  • *kumar.aanjaneya@students.iiserpune.ac.in
  • †yuvalscher@mail.tau.ac.il
  • ‡shlomire@tauex.tau.ac.il
  • §santh@iiserpune.ac.in
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Phys. Rev. Research 5, L032043 – Published 25 September, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032043

Abstract

First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions may intermittently gate our ability to observe a system of interest, such that exact first-passage instances might be missed. In other cases, e.g., certain chemical reactions, direct observation of the molecules involved is virtually impossible, but the reaction event itself can be detected. However, this instance need not coincide with the first collision time since some molecular encounters are infertile and hence, gated. Motivated by the challenge posed by such real-life situations we develop a universal—model free—framework for the inference of first-passage times from the detection times of gated first-passage processes. In addition, when the underlying laws of motions are known, our framework also provides a way to infer physically meaningful parameters, e.g., diffusion coefficients. Finally, we show how to infer the gating rates themselves via the hitherto overlooked short-time regime of the measured detection times. The robustness of our approach and its insensitivity to underlying details are illustrated in several settings of physical relevance.

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Phys. Rev. Research 5, L032043– Published 25 September, 2023
  • Received 5 October 2022
  • Revised 3 April 2023
  • Accepted 6 September 2023
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