Restricted equilibrium ensembles: Exact equation of state of a model glass

Abstract

We investigate the thermodynamic properties of a toy model of glasses: a hard-core lattice gas with nearest neighbor interaction in one dimension. The time-evolution is Markovian, with nearest-neighbor and next-nearest neighbor hoppings, and the transition rates are assumed to satisfy detailed balance condition, but the system is non-ergodic below a glass temperature. Below this temperature, the system is in restricted thermal equilibrium, where both the number of sectors, and the number of accessible states within a sector grow exponentially with the size of the system. Using partition functions that sum only over dynamically accessible states within a sector, and then taking a quenched average over the sectors, we determine the exact equation of state of this system.

6 pages, 2 figures

References in corpus (3)

• Supercooled Liquids for Pedestrians
• Glassy dynamics of kinetically constrained models
• Non-equilibrium dynamics of spin facilitated glass models

Cited by in corpus (5)

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• Glassy dynamics and hysteresis in a linear system of orientable hard rods
• Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example
• Note on specific chiral ensembles of statistical hydrodynamics: "order function" for transition of turbulence transfer scenarios
• Simulations of driven and reconstituting lattice gases