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Title:          Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
Subject:        Nature Communications 7,  (2016). doi:10.1038/ncomms12051
Author:         Jonathan Oppenheim
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        Title: Results
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          Title: Overview
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          Title: Microcanonical derivation
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        Title: Figure™1Non-Abelian thermal state.We derive the form of the thermal state of a system that has charges that might not commute with each other. Example charges include the components Ji of the spin J. We derive the thermal stateaposs form by introducing an
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        Title: Figure™2Noncommuting charges.We consider a thermodynamic system  S that has conserved charges Qj. These QjCloseCurlyQuotes might not commute with each other. The system occupies a thermal state whose form we derive. The derivation involves an approximate 
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          Title: Data availability
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        Title: GemmerJ.MichelM.MichelM.MahlerG.Quantum Thermodynamics: Emergence of Thermodynamic Behavior within Composite Quantum SystemsSpringer2009GogolinC.EisertJ.Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systemsRep
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        Title: 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 pap
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        Title: ACKNOWLEDGEMENTS
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  Checksum: f23e038a
   Type: CRC32
  Checksum: 49f42207eb6e28b300acbfbaad55eb7e
   Type: MD5
  Checksum: b651342a6b9743050c032d71ed717a52fad05490
   Type: SHA-1