Entropy production as change in observational entropy

Abstract: The second law of nonequilibrium thermodynamics within the open system paradigm (a small system coupled to one or multiple baths) is derived. This is done by showing positivity of entropy production for arbitrary Hamiltonian dynamics for a large class of initial states. Using the recently introduced notion of observational entropy, shortcomings of previous approaches are overcome. I apologize that the actual abstract of the manuscript is longer than the arXiv guidelines allow and therefore not displayed here.