Nonequilibrium dynamics of urn models

Details Nonequilibrium dynamics of urn models Nonequilibrium dynamics of urn models

2001-09-12

arxiv.org/abs/cond-mat/0109213v1

J. Phys. Cond. Matter 14, 1601 (2002)

Physics

Condensed Matter

Statistical Mechanics

15 pages. Contribution to the Proceedings of the ESF SPHINX meeting `Glassy behaviour of kinetically constrained models' (Barc

Scientific paper

10.1088/0953-8984/14/7/317

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.

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