Entropy Dynamics in the System of Interacting Qubits

The classical second law of thermodynamics demands that an isolated system evolves with a nondiminishing 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 nonunital channel can, in principle, decrease. Here, we analyze the behavior of 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. Further we discuss how small initial correlations between a quantum system and a reservoir affect the entropy increase during the quantum-system evolution.