Relaxation in non-Markovian models: From static to dynamic heterogeneity

Glass transition processes have often been explained in terms of wide distributions of relaxation times. By means of a simple stochastic model we here show how dynamic heterogeneity is the key to the emergence of the glass transition. A non-Markovian model representing a small open region of the amorphous material was previously shown to reproduce the time and thermal characteristic behavior of supercooled liquids and glasses. Due to the interaction of the open regions with their environment, the temperature dependence of the equilibrium relaxation times differs from the featureless behavior of the relaxation times of closed regions, whose static disorder does not lead to a glass transition, even with wider distributions of equilibrium relaxation times. The dynamic heterogeneity of the open region produces a glass transition between two different regimes: a faster-thanArrhenius and non-diverging growth of the supercooled liquid relaxation times and an average Arrhenius behavior of the ideal glass. The Kovacs' expansion gap was studied by evaluating the nonequilibrium distribution of relaxation times after the temperature quenches.