Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

Martin R. Evans (1) , Satya N. Majumdar (2) , Kirone Mallick (3)

1 SUPA School of Physics and Astronomy [Edinburgh]
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Martin R. Evans, Satya N. Majumdar, Kirone Mallick. Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics. Journal of Physics A: Mathematical and Theoretical, 2013, 46, pp.185001. ⟨10.1088/1751-8113/46/18/185001⟩. ⟨hal-00825684⟩