is the dissipative part describing implicitly through system operators V n the influence of the bath on the system. The Markov property imposes that the system and bath are uncorrelated at all times ρ ρ S B = ρ ρ S ⊗ ⊗ ρ ρ B . The GKSL equation is unidirectional and leads any initial state ρ ρ S to a steady state solution which is an invariant of the equation of motion ρ ρ ˙ ˙ S ( t → → ∞ ∞ ) = 0 . The family of maps generated by the GKSL equation forms a Quantum dynamical semigroup. In some fields, such as quantum optics, the term Lindblad superoperator is often used to express the quantum master equation for a dissipative system. E.B. Davis derived the GKSL with Markovian property master equations using perturbation theory and additional approximations, such as the rotating wave or secular, thus fixing the flaws of the Redfield equation. Davis construction is consistent with the Kubo-Martin-Schwinger stability criterion for thermal equilibrium i.e. the KMS state. An alternative approach to fix the Redfield has been proposed by J. Thingna, J.-S. Wang, and P. Hänggi that allows for system-bath interaction to play a role in equilibrium differing from the KMS state.