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

TL;DR

This paper derives the exact equation of state for a one-dimensional lattice glass model in restricted thermal equilibrium, revealing thermodynamic properties of non-ergodic glassy states through a sector-based partition function approach.

Contribution

It introduces a method to compute the exact thermodynamics of a non-ergodic glass model using sector-based partition functions and quenched averaging.

Findings

Exact equation of state derived for the model

Demonstrates non-ergodic behavior below glass temperature

Provides insights into restricted equilibrium in glasses

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.