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In this paper we review a recent proposal to understand the long time limitof glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantagesof the resulting construction are many. The first one is that it gives a quasiequilibrium description on how glassy systems explore the phase space in theslow relaxation part of their dynamics. The second one is that it gives analternative way to obtain dynamical equations starting from a dynamical rulethat is static in spirit. This provides a way to overcome the difficultiesencountered in the short time part of the dynamics where current conservationmust be enforced. We study this approach in detail in a prototypical mean fielddisordered spin system, namely the p-spin spherical model, showing how we canobtain the well known equations that describes its dynamics. Then we apply thesame approach to structural glasses. We first derive a set of dynamicalOrnstein-Zernike equations which are very general in nature. Finally weconsider two possible closure schemes for them, namely the Hypernetted Chainapproximation of liquid theory and a closure of the BBGKY hierarchy that hasbeen recently introduced by G. Szamel. From both approaches we finally find aset of dynamical Mode-Coupling like equations that are supposed to describe thesystem in the long time/slow dynamics regime.

Quasi equilibrium construction for the long time limit of glassy dynamics