  Volume and enthalpy relaxation of glasses after a sudden temperature change
has been extensively studied since Kovacs seminal work. One observes an
asymmetric approach to equilibrium upon cooling versus heating and, more
counter-intuitively, the expansion gap paradox, i.e. a dependence on the
initial temperature of the effective relaxation time even close to equilibrium
when heating. Here we show that a distinguishable-particles lattice model can
capture both the asymmetry and the expansion gap. We quantitatively
characterize the energetic states of the particles configurations using a
physical realization of the fictive temperature called the structural
temperature, which, in the heating case, displays a strong spatial
heterogeneity. The system relaxes by nucleation and expansion of warmer mobile
domains having attained the final temperature, against cooler immobile domains
maintained at the initial temperature. A small population of these cooler
regions persists close to equilibrium, thus explaining the paradox.
