  An operator equality on the entropy production for general quantum Markovian
master equations is derived without resorting quantum stochastic trajectory and
priori quantum definition of entropy production. We find that, the equality can
be still interpreted as a consequence of time-reversal asymmetry of the
nonequilibrium processes of the systems. In contrast with the classical case,
however, the first order expansion of the equality does not directly related to
the mean entropy production, which arises from noncommute property of operators
in quantum physics.
