  We define restricted ensembles, called pico-canonical ensembles, for a
statistical-mechanical description of the metastable and glassy phases. In this
approach, time-evolution is Markovian, with temperature dependent rates. Below
a particular glass-temperature, the system is strongly non-ergodic, and the
phase space breaks up into a large number of mutually disconnected sectors.
Averages are calculated over states within one such sector, and then averaged
over sectors. As a soluble example, we calculate these explicitly for a one
dimensional lattice gas with nearest neighbor couplings.
