Eur. Phys. J. B 23, 473-486 (2001)
https://doi.org/10.1007/s100510170039

Nonequilibrium dynamics of the zeta urn model

¹ Service de Physique de l'État Condensé, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
² Service de Physique Théorique (URA 2306 of CNRS) , CEA Saclay, 91191 Gif-sur-Yvette Cedex, France

Corresponding authors: ^a godreche@spec.saclay.cea.fr - ^b luck@spht.saclay.cea.fr

Received: 14 June 2001
Published online: 15 October 2001

Abstract

We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase, separated by a critical line. We present an analytical study of the nonequilibrium properties of the fluctuating number of balls in a given urn, considering successively the temporal evolution of its distribution, of its two-time correlation and response functions, and of the associated fluctuation-dissipation ratio, both along the critical line and in the condensed phase. For well separated times the fluctuation-dissipation ratio admits non-trivial limit values, both at criticality and in the condensed phase, which are universal quantities depending continuously on temperature.