限制平衡系综：模型玻璃的精确状态方程
Restricted equilibrium ensembles: Exact equation of state of a model glass
摘要：
我们研究了一个玩具玻璃模型的热力学性质：一个具有一维近邻相互作用的硬核格子气。时间演化是马尔可夫的，具有最近邻和次最近邻跳跃，跃迁速率被假定为满足细致平衡条件，但系统在低于玻璃温度时是非遍历的。低于该温度，系统处于受限热平衡，其中扇区的数量和扇区内可访问状态的数量都随着系统的大小呈指数增长。使用配分函数，只在一个部门内的动态可访问的状态，然后采取淬火平均的部门，我们确定了这个系统的状态方程的确切。
英文摘要：
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.
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