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Entropy production as change in observational entropy
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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.
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Typical and extreme entropies of long-lived isolated quantum systems
In a small fermionic lattice, observational entropy matches Boltzmann-like behavior at its extreme values, while entanglement entropy can fall to near zero by emptying a subsystem.
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