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Nonequilibrium dynamics of urn models

C. Godreche·J. M. Luck
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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.

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C. Godreche, J. M. Luck. 2001-09-12. Nonequilibrium dynamics of urn models. https://doi.org/10.1088/0953-8984%2F14%2F7%2F317

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