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 L-GKS 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 .