Optimal resetting mediated universal fluctuations in conditional first-passage times: Application to diffusive transport processes

Brownian motion has played a pivotal role in the foundational development of thermodynamics and statistical physics. Over the century, it has been realized that the Brownian motion can characterize the ubiquitous fluctuations of extended systems in natural and fundamental processes with widespread applications to physics, chemistry, biology, finance, and social sciences. An important cornerstone of the Brownian motion is the first-passage probability, the probability that a diffusing particle reaches a certain location for the first time, which is one key aspect of the first-passage time phenomena. Recently, a generic first-passage process which is further subject to a non-equilibrium intermittent mechanism, namely resetting, has become immensely popular due to its ability to optimize the mean first-passage time across various stochastic and natural systems. In this paper, we show that resetting can also reduce the mean completion time of a first-passage process, which has multiple competitive outcomes or exit possibilities. Conditioned on the specific choice of the exit pathway, we discover that resetting can render the relative fluctuations universal at an optimal resetting rate that emanates from a universal equality. This universality, remarkably, does not depend on the specific nature of the underlying process, the number of exit pathways, or the dimensionality of the systems of interest. Finally, we demonstrate this universal relation for simple diffusion and a diffusive transport process confined inside a channel with two exit points.