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  • Perspective
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Noncommuting conserved charges in quantum thermodynamics and beyond

Abstract

Thermodynamic systems typically conserve quantities (known as charges) such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on the failure of observables to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Noncommutation of charges has been found to invalidate derivations of the form of the thermal state, decrease entropy production, conflict with the eigenstate thermalization hypothesis and more. This Perspective surveys key results in, opportunities for and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

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Fig. 1: Common thermodynamic paradigm.
Fig. 2: Example thermodynamic system that conserves noncommuting charges.
Fig. 3: Two thermal reservoirs (A and B) exchange charges, producing entropy.
Fig. 4: Analogous noncommuting-charge and commuting-charge models.

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Acknowledgements

This work received support from the John Templeton Foundation (award no. 62422) and the National Science Foundation (QLCI grant OMA-2120757). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation or the University of Maryland. S.M. received support from the Vanier Canada Graduate Scholarships. T.U. acknowledges the support of the Joint Center for Quantum Information and Computer Science through the Lanczos Fellowship, as well as the Natural Sciences and Engineering Research Council of Canada, through the Doctoral Postgraduate Scholarship. N.Y.H. thanks the Institut Pascal for its hospitality during the formation of this paper, M. Fagotti for the discussions about GGEs, N. Mueller for the discussions about lattice gauge theories and hydrodynamics and C.D. White for MBL discussions.

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All authors contributed to the literature review for, and the drafting of, this work. N.Y.H. also contributed to the basic idea, organization and editing. S.M. handled much of the logistics.

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Correspondence to Shayan Majidy or Nicole Yunger Halpern.

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Majidy, S., Braasch, W.F., Lasek, A. et al. Noncommuting conserved charges in quantum thermodynamics and beyond. Nat Rev Phys 5, 689–698 (2023). https://doi.org/10.1038/s42254-023-00641-9

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