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  • Perspective
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Noncommuting conserved charges in quantum thermodynamics and beyond

Nature Reviews Physics volume 5, pages 689–698 (2023)Cite this article

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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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Authors and Affiliations

  1. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada

    Shayan Majidy

  2. Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada

    Shayan Majidy

  3. Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, MD, USA

    William F. Braasch Jr., Aleksander Lasek, Twesh Upadhyaya & Nicole Yunger Halpern

  4. Department of Physics, University of Maryland, College Park, MD, USA

    Twesh Upadhyaya

  5. Information Sciences Institute, University of Southern California, Arlington, VA, USA

    Amir Kalev

  6. Department of Physics and Astronomy, University of Southern California, Los Angeles, CA, USA

    Amir Kalev

  7. Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA

    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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