Entropy barriers and accelerated relaxation under resetting

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. The resetting configuration of the model, corresponding to the fixed unit resetting position of the random walker, maximises the number of boxes containing just one particle. In the limit of a large system, the relaxation time of the balls-in-boxes model under resetting is finite. The backgammon model is then studied under constant resetting using an adiabatic approximation.