Entropy barriers and accelerated relaxation under resetting

Abstract

The zero-temperature limit of the backgammon model under resetting is studied. The model is a balls-in-boxes model whose relaxation dynamics is governed by the density of boxes containing just one particle. As these boxes become rare at large times, the model presents an entropy barrier. As a preliminary step, a related model with faster relaxation, known to be mapped to a symmetric random walk, is studied by mapping recent results on diffusion with resetting onto the balls-in-boxes problem. Diffusion with an absorbing target at the origin (and diffusion constant equal to one), stochastically reset to the unit position, is a continuum approximation to the dynamics of the balls-in-boxes model, with resetting to a configuration maximising the number of boxes containing just one ball. In the limit of a large system, the relaxation time of the balls-in-boxes model under resetting is finite. The backgammon model subject to a constant resetting rate is then studied using an adiabatic approximation.