Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System

Abstract

In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $\xi$ that increases rapidly with lowering the temperature and which determines the $\alpha$-relaxation time ${\tau }_{\alpha }$ as ${\tau }_{\alpha }\sim \exp (\mu \xi /T)$ with $\mu$ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.

4 pages, 6 figures

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• Non-Equilibrium Phase Transition in an Atomistic Glassformer: the Connection to Thermodynamics
• Locally favoured structures and dynamic length scales in a simple glass-former
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• Spatial correlations of elementary relaxation events in glass-forming liquids
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• The Effective Temperature in Elasto-Plasticity of Amorphous Solids
• Jamming transition of kinetically-constrained models in rectangular systems
• Predictive Statistical Mechanics for Glass Forming Systems
• Connecting Relaxation Time to a Dynamical Length Scale in Athermal Active Glass Formers
• Jamming by Shape in Kinetically-Constrained Models
• Building a "trap model" of glassy dynamics from a local structural predictor of rearrangements
• Specific heat anomaly in a supercooled liquid with amorphous boundary conditions
• Yielding of a Model Glassformer: an Interpretation with an Effective System of Icosahedra
• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids