“Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables.
G. B. Lesovik, A. V. Lebedev, I. A. Sadovskyy, M. V. Suslov & V. M. Vinokur, “H-theorem in Quantum Physics“, Scientific Reports 6, Article number: 32815 (2016).