Nonequilibriumdynamics of urn models

Abstract

Dynamical urn models, such as the Ehrenfest model, playedan important role in the early days of statistical mechanics.Dynamical many-urn models generalize the former models in tworespects: the number of urns is macroscopic, and thermal effectsare included. These many-urn models are exactly solvable in themean-field geometry. They allow analytical investigations of thecharacteristic features of nonequilibrium dynamics referred toas aging, including the scaling of correlation and responsefunctions in the two-time plane and the violation of thefluctuation-dissipationtheorem. This paper contains a general presentation of thesemodels, as well as a more detailed description of two dynamicalurn models, the backgammon model and the zeta urn model.