Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

We study rst-passage time problems for a diusive particle with stochastic resetting with a nite rate r. The optimal search time is compared quantitatively with that of an eective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more ecient 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.

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