Axiomatic characterization of the quantum relative entropy and free energy

Understand

Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii) additivity under tensor products, and iv) super-additivity.

• This observation has immediate implications for quantum thermodynamics, which we discuss.
• Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality.
• In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand.