TY - JOUR

T1 - Entropy barriers and accelerated relaxation under resetting

AU - Grange, Pascal

N1 - Publisher Copyright:
© 2020 IOP Publishing Ltd.

PY - 2020/9/18

Y1 - 2020/9/18

N2 - 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.

AB - 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.

KW - Entropy barriers

KW - Random walks

KW - Resetting

UR - http://www.scopus.com/inward/record.url?scp=85090895101&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab94ee

DO - 10.1088/1751-8121/ab94ee

M3 - Article

AN - SCOPUS:85090895101

SN - 1751-8113

VL - 53

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 37

M1 - 375002

ER -