In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the treatment of entropy in each of classical statistical physics, Dirac's formalism of Quantum Mechanics, large systems of quantum statistical physics, and finally also for Quantum Field Theory.

This version fills a gap in the proof of Theorem 4.2 as published in Adv. Theor. Math. Phys. vol. 24, 491-526, 2020, where there was a mistake in the final paragraph of the proof. This also affected the formulation of Theorem 4.5 and proof of Theorem 5.6. The new version includes all the necessary fixes