Metastate

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. Two different versions have been proposed: 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. 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 thermodynamic states, where the system is in metastable state (for example superheating or undercooling liquids, when the actual temperature are above or below the boiling or freezing temperature, but the material is still in liquid state).