Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

TL;DR

This paper compares nonequilibrium stochastic resetting and equilibrium Langevin dynamics in diffusive search problems, demonstrating that nonequilibrium resetting generally yields faster search times and better target survival probabilities.

Contribution

It provides a quantitative comparison showing nonequilibrium resetting outperforms equilibrium dynamics in search efficiency, extending results to multiparticle systems.

Findings

Nonequilibrium resetting reduces mean first-passage time.

Target survival probability is lower with nonequilibrium dynamics.

Nonequilibrium strategies outperform equilibrium in multiparticle searches.

Abstract

We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more efficient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.