title: Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges.
abstract: 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.
authors.affiliation: Institute for Quantum Information and Matter, Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Nicole
authors.initials: N
authors.lastname: Yunger Halpern
authors.affiliation: Institute for Theoretical Physics, Department of Physics, ETH Zürich, 8093 Zürich, Switzerland.
authors.forename: Philippe
authors.initials: P
authors.lastname: Faist
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Oppenheim
authors.affiliation: Departament de Física, Grup d'Informació Quántica, Universitat Autònoma de Barcelona, ES-08193 Barcelona, Spain.|ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain.
authors.forename: Andreas
authors.identifier: 0000-0001-6344-4870
authors.initials: A
authors.lastname: Winter