Non-Abelian transport distinguishes three usually equivalent notions of entropy production

Abstract: 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 [1]. 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, an information-theoretic uncertainty measure, and 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 quivalence. Furthermore, different formulae quantify different physical effects of charges’ noncommutation on entropy production. This work opens the door of stochastic thermodynamics to charges that are peculiarly quantum by failing to commute with each other.

mathematical physicsgeneral physicsquantum physics

Audience: researchers in the topic

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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