Equation of state of a model glass

Traditionally, glasses are treated as non-equilibrium states  of matter, very slowly relaxing to equilibrium.  However, on the time-scale of milliseconds to years,  the window glass appears to be in some kind of thermal equilibrium, and it should be possible to calculate its properties theoretically, from the basic principles of statistical mechanics.

The standard method of determining properties like equation of state  of matter in equilibrium stat-mech using  the canonical partition functions  only gives the properties of crystalline quartz, and not of glass.  One needs to modify the prescription, and make only a restricted sum over states.  While the idea of restricted ensembles is not new,  it has not been possible so far  to actually calculate such restricted partition  functions  in any  non-trivial case  exactly.  I will describe a simple model of interacting particles, which shows a  glassy phase,  and where the  exact equation of state  can be determined.