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An operator equality on the entropy production for general quantum Markovianmaster equations is derived without resorting quantum stochastic trajectory andpriori quantum definition of entropy production. We find that, the equality canbe still interpreted as a consequence of time-reversal asymmetry of thenonequilibrium processes of the systems. In contrast with the classical case,however, the first order expansion of the equality does not directly related tothe mean entropy production, which arises from noncommute property of operatorsin quantum physics.

Operator equality on entropy production in quantum Markovian master equations