Understanding relaxation times in supercooled liquids and glasses

We formulate models of segmental relaxation in glasses and supercooled liquids in terms of Poisson processes and stochastic resetting and analyze their properties. This mathematical language allows us to set forth clear, consistent definitions for the various terms used throughout the literature on glassy dynamics. We provide useful algorithms for stochastic simulations of such models and show how they may be properly parameterized from time autocorrelation functions (ACFs), obtained by either simulation or experiment. Interestingly, we find that the time derivative of an ACF provides considerable insight into the distribution of relaxation times or rates and is, therefore, the primary object of analysis. These results allow for physically and mathematically robust modeling of segmental dynamics in molecular and polymeric glasses.