Resetting optimized competitive first-passage outcomes in non-Markovian systems

TL;DR

This paper explores how stochastic resetting influences first-passage processes in non-Markovian systems with memory effects, providing insights into controlling outcomes and fluctuations in complex environments.

Contribution

It introduces a framework for analyzing resetting in non-Markovian systems using CTRW, revealing how resetting can optimize and regulate first-passage events and their variability.

Findings

Resetting can selectively enhance desired first-passage outcomes.

The impact of resetting depends critically on waiting-time statistics.

An inequality quantifies how resetting suppresses fluctuations in first-passage times.

Abstract

We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time random walk (CTRW) framework, we analyze first-passage processes with multiple competing outcomes and examine how resetting can selectively enhance desired events. We characterize the efficiency of resetting through conditional mean first-passage times (MFPTs) and demonstrate that its impact is highly sensitive to the underlying waiting-time statistics. Furthermore, we derive an inequality that quantifies how resetting controls fluctuations in conditional first-passage times (FPTs), revealing regimes where variability is significantly suppressed. Our results provide a systematic understanding of how long-term memory influences competitive first-passage outcomes and establish resetting as a powerful control mechanism beyond the conventional Markovian setting.