Metastate
In statistical mechanics, the metastate is a probability measure on the
space 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 varying
the random parameters in the Hamiltonian outside of the volume being
considered.
2) The Newman-Stein metastate, a microcanonical ensemble approach,
constructs an empirical average from a deterministic subsequence of finite-volume Gibbs distributions.
It was proved for Euclidean lattices that there always
exists a deterministic subsequence along which the Newman-Stein and
Aizenman-Wehr constructions result in the same metastate. The metastate is
especially useful in systems where deterministic sequences of volumes fail
to converge to a thermodynamic state, and/or there are many competing
observable thermodynamic states.
As an alternative usage, "metastate" can refer thermodynamic states, where the system is in metastable state.
