Catalytic quantum thermodynamics beyond additivity and reduced-state monotones

TL;DR

This paper introduces a non-additive divergence framework in quantum thermodynamics that explicitly accounts for catalytic contributions, revealing limitations of reduced-state data in characterizing thermodynamic transformations.

Contribution

It develops a non-additive divergence-based formulation that explicitly incorporates catalysts and demonstrates the insufficiency of reduced-state data in correlated catalysis.

Findings

Non-additive second-law relations make catalytic contributions explicit.

Reduced-state data are insufficient to determine thermodynamic accessibility.

Correlated catalysis requires joint-state-sensitive descriptions beyond monotones.

Abstract

The generalized second laws of quantum thermodynamics are usually formulated in terms of R\'enyi divergences and the associated family of generalized free energies. In catalytic thermal transformations, this framework typically certifies the existence of a suitable catalyst but does not make the catalytic contribution explicit in the resulting system-level inequalities. Here we develop a complementary formulation based on non-additive divergences, whose pseudo-additive structure yields a family of generalized free energies with an explicit catalyst-dependent correction term. For uncorrelated catalytic thermal transformations, we show that this leads to non-additive second-law relations that make the catalytic contribution explicit and provide nontrivial constraints on admissible catalysts when the catalyst is returned only approximately. We also analyze correlated catalytic thermal transformations and show, through explicit finite-dimensional examples, that reduced-state data are generally insufficient to characterize thermodynamic accessibility: the thermo-majorization behavior of the joint transformation can change while the system and catalyst marginals remain fixed, and even states with identical marginals and the same mutual information can exhibit different thermo-majorization accessibility. Our results show that non-additivity can be thermodynamically informative in uncorrelated catalysis, whereas correlated catalysis generally requires a genuinely joint-state-sensitive description beyond reduced-state monotones.