Predictive statistical mechanics for glass forming systems

Abstract

Using two extremely different models of glass formers in two and three dimensions wedemonstrate how to encode the subtle changes in the geometric rearrangement ofparticles during the scenario of the glass transition. We construct a statisticalmechanical description that is able to explain and predict the geometricrearrangement, the temperature-dependent thermodynamic functions and theα-relaxation time within the measured temperature range and beyond. The theory is basedon an up-scaling to proper variables (quasi-species) which is validated using a simplecriterion. Once constructed, the theory provides an accurate predictive tool for quantitieslike the specific heat or the entropy at temperatures that cannot be reached bymeasurements. In addition, the theory identifies a rapidly increasing typical length scaleξ as the temperature decreases. This growing spatial length scale determines theα-relaxationtime as τα∼exp(μξ/T), where μ is a typical chemical potential per unit length.