Optimal stochastic restart renders fluctuations in first passage times universal

TL;DR

This paper demonstrates that for processes optimized with stochastic restart to minimize mean first passage time, the relative standard deviation of the FPT is universally equal to one, revealing a fundamental fluctuation property.

Contribution

It establishes a universal fluctuation law for optimally restarted stochastic processes, linking mean minimization to a fixed relative variability.

Findings

Relative standard deviation of FPT at optimal restart is always one.

Universal fluctuation property across diverse first-passage-time processes.

Implications for designing efficient stochastic algorithms and reactions.

Abstract

Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT) processes seem to have very little in common but it is actually quite the other way around. Here we show that the relative standard deviation associated with the FPT of an optimally restarted process, i.e., one that is restarted at a (non-zero) rate which brings the mean FPT to a minimum, is always unity. We interpret, further generalize, and discuss this finding and the implications arising from it.