# Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System - Condensed Matter > Statistical Mechanics

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Abstract: In the context of a classical example of glass-formation in 3-dimensions weexemplify how to construct a statistical mechanical theory of the glasstransition.
At the heart of the approach is a simple criterion for verifying aproper choice of up-scaled quasi-species that allow the construction of atheory with a finite number of -states-.
Once constructed, the theoryidentifies a typical scale $\xi$ that increases rapidly with lowering thetemperature and which determines the $\alpha$-relaxation time $\tau \alpha$ as$\tau \alpha \sim \exp\mu\xi-T$ with $\mu$ a typical chemical potential.
Thetheory can predict relaxation times at temperatures that are inaccessible tonumerical simulations.

Author: Edan Lerner, Itamar Procaccia, Jacques Zylberg

Source: https://arxiv.org/