Nonequilibrium dynamics of urn models

Abstract

Dynamical urn models, such as the Ehrenfest model, have played an important role in the early days of statistical mechanics. Dynamical many-urn models generalize the former models in two respects: the number of urns is macroscopic, and thermal effects are included. These many-urn models are exactly solvable in the mean-field geometry. They allow analytical investigations of the characteristic features of nonequilibrium dynamics referred to as aging, including the scaling of correlation and response functions in the two-time plane and the violation of the fluctuation-dissipation theorem. This review paper contains a general presentation of these models, as well as a more detailed description of two dynamical urn models, the backgammon model and the zeta urn model.Comment: 15 pages. Contribution to the Proceedings of the ESF SPHINX meeting `Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001). To appear in a special issue of J. Phys. Cond. Mat