Pico-canonical ensembles: a theoretical description of metastable states

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.