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

TL;DR

This paper extends the concept of entropy production to quantum systems with noncommuting conserved charges, revealing that noncommutation breaks the equivalence of common entropy formulas and introduces uniquely quantum effects.

Contribution

It generalizes three standard entropy production formulas to noncommuting charges and demonstrates their non-equivalence and quantum-specific implications.

Findings

Noncommutation breaks the equivalence of entropy formulas.

Entropy production can become nonreal, indicating quantum contextuality.

The work extends stochastic thermodynamics to quantum charges.

Abstract

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, 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 up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.