Additional conditions have to be imposed on the dissipator L D to be consistent with thermodynamics. First the invariant ρ ρ S ( ∞ ∞ ) should become an equilibrium Gibbs state. This implies that the dissipator L D should commute with the unitary part generated by H S . In addition an equilibrium state is stationary and stable. This assumption is used to derive the Kubo-Martin-Schwinger stability criterion for thermal equilibrium i.e. KMS state.