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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.〔Newman, C. M.; Stein, D. L. (1996), ''Spatial inhomogeneity and thermodynamic chaos'', Phys. Rev. Lett., Vol. 76: 4821-4824.〕 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.〔Aizenman, M.; Wehr, J. (1990), ''Rounding effects of quenched randomness on first-order phase transitions'', Commun. Math. Phys., Vol. 130: 489-528.〕 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.〔〔Newman, C. M.; Stein, D. L. (1997), ''Metastate approach to thermodynamic chaos'', Phys. Rev. E, Vol. 55: 5194-5211.〕〔Newman, C. M.; Stein, D. L. (1998). "Thermodynamic chaos and the structure of short-range spin glasses." in A. Bovier and P. Picco. ''Mathematics of Spin Glasses and Neural Networks.'' Boston: Birkhauser. pp. 243-247.〕 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. ==References== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Metastate」の詳細全文を読む スポンサード リンク
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