Metastate
Introduction In statistical mechanics, the '''metastate''' is a probability measure on thespace of all thermodynamic states for a system with quenched randomness. The term metastate, in this context, was first used in by Charles M. Newman and Daniel L. Stein in 1996.. Two different versions have been proposed:1) The Aizenman-Wehr construction, a canonical ensemble approach,constructs the metastate through an ensemble of states obtained by varyingthe random parameters in the Hamiltonian outside of the volume beingconsidered.2) The Newman-Stein metastate, a microcanonical ensemble approach,constructs an empirical average from a deterministic (i.e., chosenindependently of the randomness) subsequence of finite-volume Gibbs distributions.It was proved for Euclidean lattices that there alwaysexists a deterministic subsequence along which the Newman-Stein andAizenman-Wehr constructions result in the same metastate. The metastate isespecially useful in systems where deterministic sequences of volumes failto converge to a thermodynamic state, and/or there are many competingobservable thermodynamic states.As an alternative usage, "metastate" can refer to thermodynamic states, where the system is in a metastable state (for example  superheated or undercooled liquids, when the actual temperature of the liquid is above or below the boiling or freezing temperature, but the material is still in a liquid state).
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