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

Published

May 24, 2023

Author(s)

Twesh Upadhyaya, William Braasch, Gabriel Landi, Nicole Halpern

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.

Citation

arXiv

Pub Weblink

https://arxiv.org/abs/2305.15480

Pub Type

Websites

Keywords

Quantum thermodynamics, noncommuting conserved quantities, stochastic entropy production

Citation

Upadhyaya, T. , Braasch, W. , Landi, G. and Halpern, N. (2023), What happens to entropy production when conserved quantities fail to commute with each other, arXiv, [online], https://arxiv.org/abs/2305.15480 (Accessed February 14, 2026)