Search with stochastic home returns can expedite classical first passage under resetting

Area of Science:

• Statistical Physics
• Stochastic Processes
• Complex Systems

Background:

• Classical first passage time problems are crucial in search processes across various scientific fields.
• Experimental implementation of instantaneous resetting poses significant calibration challenges.
• Finite-time return protocols offer an alternative to instantaneous resetting in search strategies.

Purpose of the Study:

• To develop a unified renewal approach for analyzing search processes with finite-time resetting.
• To investigate the potential for speed-up in search processes using finite-time return protocols.
• To establish a universal criterion for optimizing search strategies with inherent randomness.

Main Methods:

• Development of a unified renewal approach applicable to general topographies and dimensions.
• Modeling of search processes with arbitrary targets, resetting times, and return mechanisms.
• Analysis of finite-time return protocols, including those with random fluctuations.

Main Results:

• Finite-time resetting, contrary to initial intuition, can significantly accelerate search times.
• Stochasticity during home returns is key to achieving search speed-up.
• A universal criterion for evaluating the benefits of finite-time resetting strategies was identified.

Conclusions:

• Finite-time resetting protocols with inherent randomness offer an effective strategy for optimizing complex search processes.
• The developed renewal approach provides a general framework for analyzing such processes.
• Experimental feasibility is enhanced by incorporating controllable randomness into return mechanisms.