Smart Resetting: An Energy-Efficient Strategy for Stochastic Search Processes

TL;DR

This paper introduces 'smart resetting', an energy-efficient strategy for stochastic search processes that uses information to minimize energy costs and outperforms regular resetting in diffusive systems.

Contribution

It analytically demonstrates that smart resetting reduces energetic costs compared to regular resetting and extends the concept to nonlinear costs and drift-diffusion processes.

Findings

Smart resetting lowers energy costs compared to regular resetting.

It achieves the minimum energy cost previously known for regular resetting.

The strategy extends to nonlinear cost functions and drift-diffusion models.

Abstract

Stochastic resetting, a method for accelerating target search in random processes, often incurs temporal and energetic costs. For a diffusing particle, a lower bound exists for the energetic cost of reaching the target, which is attained at low resetting rates and equals the direct linear transportation cost against fluid drag. Here, we study ``smart resetting," a strategy that aims to beat this lower bound. By strategically resetting the particle only when this benefits its progress toward the target, smart resetting leverages information to minimize energy consumption. We analytically calculate the energetic cost per mean first passage time and show that smart resetting consistently reduces the energetic cost compared to regular resetting. Surprisingly, smart resting achieves the minimum energy cost previously established for regular resetting, irrespective of the resetting rate. Yet, it fails to reduce this cost further. We extend our findings in two ways: first, by examining nonlinear energetic cost functions, and second, by considering smart resetting of drift-diffusion processes.