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]
Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which increases the substance's temperature to the melting point. At the melting point, the ordering of ions or molecules in the solid breaks down to a less ordered state, and the solid "melts" to become a liquid.
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