Uploaded February 2025 | Updated September 2026, 3 hours ago
Non-Abelian transport distinguishes three usually equivalent notions of entropy production
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. The systems can exchange some physical quantities (“charges”). There are three formulas that are commonly used to measure the entropy produced. These cast entropy as (1) an extensive thermodynamic variable, (2) an information-theoretic uncertainty measure, and (3) a quantifier of irreversibility. Typically, the charges are assumed to commute with each other (e.g., energy and particle number), meaning that they can be simultaneously measured. When this is true, the three entropy production formulas yield the same result. 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.
Non-Abelian transport distinguishes three usually equivalent notions of entropy production
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. The systems can exchange some physical quantities (“charges”). There are three formulas that are commonly used to measure the entropy produced. These cast entropy as (1) an extensive thermodynamic variable, (2) an information-theoretic uncertainty measure, and (3) a quantifier of irreversibility. Typically, the charges are assumed to commute with each other (e.g., energy and particle number), meaning that they can be simultaneously measured. When this is true, the three entropy production formulas yield the same result. 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.
