Physics: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 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
- ↑ 1.0 1.1 Newman, C. M.; Stein, D. L. (17 June 1996). "Spatial Inhomogeneity and Thermodynamic Chaos". Physical Review Letters (American Physical Society (APS)) 76 (25): 4821–4824. doi:10.1103/physrevlett.76.4821. ISSN 0031-9007. PMID 10061389. Bibcode: 1996PhRvL..76.4821N.
- ↑ Aizenman, Michael; Wehr, Jan (1990). "Rounding effects of quenched randomness on first-order phase transitions". Communications in Mathematical Physics (Springer Science and Business Media LLC) 130 (3): 489–528. doi:10.1007/bf02096933. ISSN 0010-3616. Bibcode: 1990CMaPh.130..489A. http://projecteuclid.org/euclid.cmp/1104200601.
- ↑ Newman, C. M.; Stein, D. L. (1 April 1997). "Metastate approach to thermodynamic chaos". Physical Review E (American Physical Society (APS)) 55 (5): 5194–5211. doi:10.1103/physreve.55.5194. ISSN 1063-651X. Bibcode: 1997PhRvE..55.5194N.
- ↑ 4.0 4.1 Newman, Charles M.; Stein, Daniel L. (1998). "Thermodynamic Chaos and the Structure of Short-Range Spin Glasses". Mathematical Aspects of Spin Glasses and Neural Networks. Boston, MA: Birkhäuser Boston. pp. 243–287. doi:10.1007/978-1-4612-4102-7_7. ISBN 978-1-4612-8653-0.
- ↑ Debenedetti, P.G.Metastable Liquids: Concepts and Principles; Princeton University Press: Princeton, NJ, USA, 1996.
- ↑ Imre, Attila; Wojciechowski, Krzysztof; Györke, Gábor; Groniewsky, Axel; Narojczyk, Jakub. (3 May 2018). "Pressure-Volume Work for Metastable Liquid and Solid at Zero Pressure". Entropy (MDPI AG) 20 (5): 338. doi:10.3390/e20050338. ISSN 1099-4300. PMID 33265428. Bibcode: 2018Entrp..20..338I.
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