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 by Charles M. Newman and Daniel L. Stein in 1996..[1]
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]
2) The Newman-Stein metastate, a microcanonical ensemble approach, constructs an empirical average from a deterministic (i.e., chosen independently of the randomness) subsequence of finite-volume Gibbs distributions.[1][3][4]
It was proved[4] 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 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).[5][6]
References
Wikiwand in your browser!
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.
