  The Second Law of Thermodynamics states that temporal evolution of an
isolated system occurs with non-diminishing entropy. In quantum realm, this
holds for energy-isolated systems the evolution of which is described by the
so-called unital quantum channel. The entropy of a system evolving in a
non-unital quantum channel can, in principle, decrease. We formulate a general
criterion of unitality for the evolution of a quantum system, enabling a simple
and rigorous approach for finding and identifying the processes accompanied by
decreasing entropy in energy-isolated systems. We discuss two examples
illustrating our findings, the quantum Maxwell demon and heating-cooling
process within a two-qubit system.
