treating the evolution of the system. In other words, if the interaction between the system and its environment is weak, then any changes to the combined system over time can be approximated as originating from only the system in question. Another typical assumption is that the system and bath are initially uncorrelated . This idea originated with Felix Bloch and was expanded upon by Alfred Redfield in his derivation of the Redfield equation. The Redfield equation is a Markovian master equation that describes the time evolution of the density matrix of the combined system. The drawback of the Redfield equation is that it does not conserve the positivity of the density operator. A formal construction of a local equation of motion with a Markovian property is an alternative to a reduced derivation. The theory is based on an axiomatic approach. The basic starting point is a completely positive map. The assumption is that the initial system-environment state is uncorrelated and the combined dynamics is generated by a unitary operator. Such a map falls under the category of Kraus operator. The most general type of a time-homogeneous master equation with the Markovian property describing non-unitary evolution of the density matrix ρ that is trace-preserving and completely positive for any initial condition is the Gorini–Kossakowski–Sudarshan–Lindblad equation or GKSL equation: is a (Hermitian) Hamiltonian part and : is the dissipative part describing implicitly through system operators the influence of the bath on the system. The Markov property imposes that the system and bath are uncorrelated at all times . The GKSL equation is unidirectional and leads any initial state to a steady state solution which is an invariant of the equation of motion . 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.