What happens to entropy production when conserved quantities fail to commute with each other - Billy Braasch

A fundamental challenge is to define quantum thermodynamic quantities-for example, heat, work, and entropy production. We extend the definition of entropy production to a deeply quantum regime involving noncommuting observables. Consider two systems prepared in different thermal states. A unitary transports observables ("charges") between the systems. Three common formulae model the entropy produced. They cast entropy as an extensive thermodynamic variable, as an informationtheoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number), and the entropy-production formulae equal each other. Yet quantum charges can fail to commute, inviting generalizations of the three formulae. Charges’ noncommutation, we find, breaks the formulae's equivalence. Furthermore, different formulae quantify different physical effects of charges' noncommutation on entropy production. For instance, entropy production can signal contextuality-true nonclassicality-by becoming nonreal. This work opens the door of stochastic thermodynamics to charges that are peculiarly quantum by failing to commute with each other.