Predictive Statistical Mechanics for Glass Forming Systems

TL;DR

This paper develops a statistical mechanical framework for glass formers that accurately predicts thermodynamic and dynamic properties, including relaxation times and length scales, across a range of temperatures.

Contribution

The authors introduce a novel up-scaling approach to quasi-species variables that captures geometric rearrangements and predicts properties beyond measurable temperatures.

Findings

Accurate prediction of specific heat and entropy at unmeasured temperatures.

Identification of a rapidly increasing length scale $\xi$ with decreasing temperature.

Establishment of a relation between relaxation time and length scale: $ au_eta ext{exp}(rac{ ext{ extmu}\xi}{T})$.

Abstract

Using two extremely different models of glass formers in two and three dimensions we demonstrate how to encode the subtle changes in the geometric rearrangement of particles during the scenario of the glass transition. We construct a statistical mechanical description that is able to explain and predict the geometric rearrangement, the temperature dependent thermodynamic functions and the $\alpha$-relaxation time within the measured temperature range and beyond. The theory is based on an up-scaling to proper variables (quasi-species) which is validated using a simple criterion. Once constructed, the theory provides an accurate predictive tool for quantities like the specific heat or the entropy at temperatures that cannot be reached by measurements. In addition, the theory identifies a rapidly increasing typical length scale $\xi$ as the temperature decreases. This growing spatial length scale determines the $\alpha$-relaxation time as $\tau_\alpha \sim \exp(\mu\xi/T)$ where $\mu$ is a typical chemical potential per unit length.