Which entropy increases in isolated quantum systems?

Abstract

The second thermodynamic law says that entropy increases in an isolated system. Which entropy though? The von Neumann entropy stays constant, entanglement entropy can increase, but it measures primarily quantum correlations, and Boltzmann and Gibbs entropies are defined only in equilibrium, and do not change when the system thermalizes. I will present a definition of entropy that is defined out-of-equilibrium, it generalizes equilibrium entropy to non-equilibrium situations, increases in an isolated system, and is internally connected to a quantum measurement. Thus, proposing a definition through which the second thermodynamic law is expressed, in non-equilibrium quantum systems.