Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

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

Journal of Physics A: Mathematical and Theoretical 46 (2013) 185001

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.

  • 1 : SUPA, School of Physics, University of Edinburgh
    SUPA
  • 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3 : Institut de Physique Théorique (ex SPhT) (IPHT)
    CNRS : URA2306 – CEA : DSM/IPHT