  Control of open quantum dynamics is of great interest for realizing quantum
technologies. Therefore, it is an important task to quantify and characterize
the entropy for open quantum systems under decoherence. In this paper, we study
the time evolution of the von Neumann entropy for open quantum systems
described by the Lindblad master equation. Note that, in particular, when the
decoherence corresponds to the measurement for the observable in the system,
the von Neumann entropy tends to monotonically increases as the variance
becomes larger. Furthermore, we present a lower bound of the von Neumann
entropy in the long-time limit. This lower bound has advantages of being
straightforwardly calculated and applicable to a general Markovian open quantum
system.
