Quasi-equilibrium in glassy dynamics: a liquid theory approach

We introduce a quasi-equilibrium formalism in the theory of liquids in order to obtain a set of coarse grained dynamical equations for the description of long time glassy relaxation. Our scheme allows to use typical approximations devised for equilibrium to study glassy dynamics. After introducing dynamical Ornstein-Zernike relations, we focus on the hypernetted chain (HNC) approximation and a recent closure scheme developed by Szamel. In both cases we get dynamical equations that have the structure of the mode-coupling theory (MCT) equations in the long time regime. The HNC approach, that was so far used to get equilibrium quantities is thus generalized to a fully consistent scheme where long-time dynamic quantities can also be computed. In the context of this approximation we get an asymptotic description of both equilibrium glassy dynamics at high temperature and of aging dynamics at low temperature. The Szamel approximation on the other hand is shown to lead to the canonical MCT equations obtained by Gotze for equilibrium dynamics. We clarify the way phase space is sampled according to MCT during dynamical relaxation.