  The classical Second Law of Thermodynamics demands that an isolated system
evolves with a non-diminishing entropy. This holds as well in quantum mechanics
if the evolution of the energy-isolated system can be described by a unital
quantum channel. At the same time, the entropy of a system evolving via a
non-unital channel can, in principle, decrease. Here, we analyze the behavior
of the entropy in the context of the H-theorem. As exemplary phenomena, we
discuss the action of a Maxwell demon (MD) operating a qubit and the processes
of heating and cooling in a two-qubit system. We further discuss how small
initial correlations between a quantum system and a reservoir affect the
increase in the entropy under the evolution of the quantum system.
