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Volume and enthalpy relaxation of glasses after a sudden temperature changehas been extensively studied since Kovacs seminal work. One observes anasymmetric approach to equilibrium upon cooling versus heating and, morecounter-intuitively, the expansion gap paradox, i.e. a dependence on theinitial temperature of the effective relaxation time even close to equilibriumwhen heating. Here we show that a distinguishable-particles lattice model cancapture both the asymmetry and the expansion gap. We quantitativelycharacterize the energetic states of the particles configurations using aphysical realization of the fictive temperature called the structuraltemperature, which, in the heating case, displays a strong spatialheterogeneity. The system relaxes by nucleation and expansion of warmer mobiledomains having attained the final temperature, against cooler immobile domainsmaintained at the initial temperature. A small population of these coolerregions persists close to equilibrium, thus explaining the paradox.

Spatial heterogeneities in structural temperature cause Kovacs expansion gap paradox in aging of glasses