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Many chemical reactions can be formulated in terms of particle diffusion in acomplex energy landscape. Transition path theory (TPT) is a theoreticalframework for describing the direct (reaction) pathways from reactant toproduct states within this energy landscape, and calculating the effectivereaction rate. It is now the standard method for analyzing rare events betweenlong lived states. In this paper, we consider a completely differentapplication of TPT, namely, a dual-aspect diffusive search process in which aparticle alternates between collecting cargo from a source domain $A$ and thendelivering it to a target domain $B$. The rate of resource accumulation at thetarget, $k_{AB}$, is determined by the statistics of direct (reactive ortransport) paths from A to B. Rather than considering diffusion in a complexenergy 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 thatthere exists a unique non-equilibrium stationary state (NESS). Second,calculating $k_{AB}$ involves determining the total probability flux of directtransport paths across a dividing surface $S$ between $A$ and $B$. Thisrequires taking into account discontinuous jumps across $S$ due to resetting.We derive a general expression for $k_{AB}$ and show that it is independent ofthe choice of dividing surface. Finally, using the example of diffusion in afinite interval, we show that there exists an optimal resetting rate at which$k_{AB}$ is maximized. We explore how this feature depends on model parameters.

Transition path theory for diffusive search with stochastic resetting