  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. We discuss the manifestation of the second law
of thermodynamics in quantum physics and uncover special situations where the
second law can be violated. We further demonstrate that the typical evolution
of energy-isolated quantum systems occurs with non-diminishing entropy.
