<p>The second law of thermodynamics is a fundamental concept in physics, characterizing the convertibility between thermodynamic states through a single function—entropy. An important question in quantum information theory has been whether an analogous second law can be established for resources in quantum information processing, such as entanglement. In 2008, a formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing. The proposal made use of the generalized quantum Stein’s lemma to characterize this optimal performance by a measure of quantum resources, the regularized relative entropy of resource. If this approach is valid, a second law for quantum resources can be established, with the regularized relative entropy of resource taking on the role of thermodynamic entropy. However, in 2023, a gap was found in the proof of the generalized Stein’s lemma. Here we provide an alternative proof of the generalized quantum Stein’s lemma under a smaller set of assumptions. Furthermore, we re-establish and extend the second law of quantum resource theories, applicable to both static resources of quantum states and dynamical resources represented by classical–quantum channels.</p>