In this paper we apply some theoretical predictions that arise in the mean-field framework for a large class of infinite-range models to structural glasses and we present a first comparison of these predictions with numerical results. We find evidence for the energy density relaxation at low temperatures consisting of two steps: the convergence to some metastable state with a mean-field-like behaviour and the decay of metastable states by activated processes. We define an appropriate distance d between states and we study the corresponding equilibrium distribution that results in being highly nontrivial in the glassy phase.