Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

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.