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Macroscopic and microscopic thermal equilibrium

Author(s): Goldstein, Sheldon; Huse, David A; Lebowitz, Joel L; Tumulka, Roderich

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Abstract: We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (MITE). The distinction between MITE and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ) in an energy shell, then for generic macroscopic systems, including those with MBL, most are in both MATE and MITE. We explore here the properties of MATE and MITE and compare the two notions, thereby elaborating on ideas introduced in [18].
Publication Date: 9-Feb-2017
Electronic Publication Date: Jul-2017
Citation: Goldstein, Sheldon, Huse, David A, Lebowitz, Joel L, Tumulka, Roderich. (2017). Macroscopic and microscopic thermal equilibrium. ANNALEN DER PHYSIK, 529 (10.1002/andp.201600301
DOI: doi:10.1002/andp.201600301
ISSN: 0003-3804
EISSN: 1521-3889
Type of Material: Journal Article
Journal/Proceeding Title: ANNALEN DER PHYSIK
Version: Author's manuscript

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