  A general relation between entropy and an evolutionary superoperator is
derived based on the theory of the real-time formulation. The formulation
establishing the relation relies only on the framework of quantum statistical
mechanics and the standard definition of the von Neumann entropy. Applying the
theory of the imaginary-time formulation, a similar relation is obtained for
the entropy change due to the change in reservoir temperatures. To show the
usefulness of these formulas, we derived the expression for the entropy
production induced by some dissipation in an open quantum system as the
exemplary model system.
