Thermodynamic systems typically conserve quantities ("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
observables' failure 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. Charges' noncommutation has been found to invalidate derivations of
the thermal state's form, 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.Comment: 9.5 pages (3 figures) + appendices (10 pages