The generalized second laws of quantum thermodynamics are usually formulated in terms of Rényi 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 nonadditive 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 nonadditive second-law relations providing 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.

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• Quantum statistical mechanics
• Resource theories