Transition path theory for diffusive search with stochastic resetting
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states within this energy landscape, and calculating the effective reaction rate. It is now the standard method for analyzing rare events between long lived states. In this paper, we consider a completely different application of TPT, namely, a dual-aspect diffusive search process in which a particle alternates between collecting cargo from a source domain A and then delivering it to a target domain B. The rate of resource accumulation at the target, kAB, is determined by the statistics of direct (reactive or transport) paths from A to B. Rather than considering diffusion in a complex energy landscape, we focus on pure diffusion with stochastic resetting. Resetting introduces two non-trivial problems in the application of TPT. First, the process is not time-reversal invariant, which is reflected by the fact that there exists a unique non-equilibrium stationary state (NESS). Second, calculating kAB involves determining the total probability flux of direct transport paths across a dividing surface S between A and B. This requires taking into account discontinuous jumps across S due to resetting. We derive a general expression for kAB and show that it is independent of the choice of dividing surface. Finally, using the example of diffusion in a finite interval, we show that there exists an optimal resetting rate at which kAB is maximized. We explore how this feature depends on model parameters.
Date Issued
2024-04-05
Date Acceptance
2024-03-12
Citation
Journal of Physics A: Mathematical and Theoretical, 2024, 57 (14)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
57
Issue
14
Copyright Statement
© 2024 The Author(s). Published by IOP Publishing Ltd
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Identifier
http://dx.doi.org/10.1088/1751-8121/ad330b
Publication Status
Published
Article Number
145001
Date Publish Online
2024-03-26