Non-equilibrium steady states of stochastic processes with intermittent resetting

TL;DR

This paper generalizes the understanding of non-equilibrium steady states in stochastic processes with resetting by allowing arbitrary waiting time distributions, broadening the scope beyond memoryless protocols and enabling analysis of more realistic systems.

Contribution

It provides the first general solution for the distribution of stochastic processes with arbitrary waiting time distributions between resets.

Findings

Derived the distribution for processes with arbitrary reset waiting times.

Applied results to analyze efficiency of constrained random search processes.

Extended the theoretical framework beyond memoryless resetting protocols.

Abstract

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols. Here, we obtain the general solution for the distribution of processes in which waiting times between reset events are drawn from an arbitrary distribution. This allows for the investigation of a broader class of much more realistic processes. As an example, our results are applied to the analysis of the efficiency of constrained random search processes.