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Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges

Yunger Halpern, Nicole and Faist, Philippe and Oppenheim, Jonathan and Winter, Andreas (2016) Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges. Nature Communications, 7 . Art. No. 12051. ISSN 2041-1723. PMCID PMC4941045. doi:10.1038/ncomms12051.

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The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system’s thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity—the inability to extract work from equilibrium states—implies the thermal state’s form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation.

Item Type:Article
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URLURL TypeDescription CentralArticle
Yunger Halpern, Nicole0000-0001-8670-6212
Faist, Philippe0000-0003-1696-6400
Oppenheim, Jonathan0000-0002-8993-412X
Additional Information:© 2016 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit Received 22 December 2015; Accepted 23 May 2016; Published 07 July 2016. We thank David Jennings, Tim Langen, Elliott Lieb (who pointed us to ref. 29), Matteo Lostaglio, Shelly Moram, Joseph M. Renes and Terry Rudolph for interesting conversations. We thank the authors of refs 27,28 for their community spirit. Much of this paper was developed at ‘Beyond i.i.d. in Information Theory 2015,’ hosted by BIRS. A.W.’s work was supported by the EU (STREP ‘RAQUEL’), the ERC (AdG ‘IRQUAT’), the Spanish MINECO (grant FIS2013-40627-P) with the support of FEDER funds, as well as by the Generalitat de Catalunya CIRIT, project 2014-SGR- 966. J.O. is supported by an EPSRC Established Career Fellowship, the Royal Society and FQXi. N.Y.H. was supported by an IQIM Fellowship and NSF grant PHY-0803371. The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center supported by the Gordon and Betty Moore Foundation. P.F. acknowledges support from the European Research Council (ERC) via grant No. 258932, from the Swiss National Science Foundation through the National Centre of Competence in Research ‘Quantum Science and Technology’ (QSIT), and by the European Commission via the project ‘RAQUEL.’ This work was partially supported by the COST Action MP1209. Author contributions: All authors contributed to all aspects of this work. Competing financial interests: The authors declare no competing financial interests.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
European Union (EU)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Ministerio de Economía y Competitividad (MINECO)FIS2013-40627-P
Fonds Européen de Développement Économique et Régional (FEDER)UNSPECIFIED
Generalitat de Catalunya2014-SGR-966
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Foundational Questions Institute (FQXI)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
European Research Council (ERC)258932
Swiss National Science Foundation (SNSF)UNSPECIFIED
European CommissionUNSPECIFIED
COST ActionMP1209
PubMed Central ID:PMC4941045
Record Number:CaltechAUTHORS:20160718-105044441
Persistent URL:
Official Citation:Yunger Halpern, N. et al. Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges. Nat. Commun. 7:12051 doi: 10.1038/ncomms12051 (2016)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69093
Deposited By: Tony Diaz
Deposited On:19 Jul 2016 22:05
Last Modified:26 Apr 2022 17:07

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