text: When  the first law of thermodynamics emerges:
  where power is interpreted as 
  and the heat current .
  Additional conditions have to be imposed on the dissipator  to be consistent with thermodynamics.
  First the invariant  should become an equilibrium Gibbs state.
  This implies that the dissipator  should commute with the unitary part generated by . 
  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.
  A unique and consistent approach is obtained by deriving the generator, , in the weak system bath
  coupling limit.
  In this limit, the interaction energy can be neglected. This approach represents a thermodynamic idealization: it allows energy transfer, while keeping a tensor product separation
  between the system and bath, i.e., a quantum version of an isothermal partition.
  Markovian behavior involves a rather complicated cooperation between system and bath dynamics. This means that in
  phenomenological treatments, one cannot combine arbitrary system Hamiltonians, , with a given L-GKS generator. This observation is particularly important in the context of quantum thermodynamics,
  where it is tempting to study Markovian dynamics with an arbitrary control Hamiltonian. Erroneous derivations of the quantum master equation can easily lead to a violation of the laws of thermodynamics.
  An external perturbation modifying the Hamiltonian of the system will also modify the heat flow. As a result, the L-GKS generator has to be renormalized. For a slow change, one can adopt the adiabatic approach and use the instantaneous system’s Hamiltonian to derive . An important class of problems in quantum thermodynamics is periodically driven systems. Periodic quantum heat engines and power-driven refrigerators fall into this class.
  A reexamination of the time-dependent heat current expression using quantum transport techniques has been proposed.
  A derivation of consistent dynamics beyond the weak coupling limit has been suggested.
  Phenomenological formulations of irreversible quantum dynamics consistent with the second law and implementing the geometric idea of "steepest entropy ascent" or "gradient flow" have been suggested to model relaxation and strong coupling.