  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.
