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Nonequilibrium dynamics of the zeta urn model

C. Godreche·J. M. Luck
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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 \fd ratio, both along the critical line and in the condensed phase. For well separated times the \fd ratio admits non-trivial limit values, both at criticality and in the condensed phase, which are universal quantities depending continuously on temperature.

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C. Godreche, J. M. Luck. 2001-06-14. Nonequilibrium dynamics of the zeta urn model. https://doi.org/10.1007/s100510170039

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