Open system dynamics from thermodynamic compatibility

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the map of the system's unitary evolution. Employing spectral analysis, we prove the general form of the ensuing master equation. The obtained structure extends thermodynamical considerations to dynamical processes. Comparing this form with master equations obtained from microscopic derivations allows validating their compatibility with thermodynamics. It predicts that coherence is not generated spontaneously under steady-state transport. Moreover, for a bipartite system-environment it singles out the global master equation as the thermodynamically compatible choice for nondriven systems, as well as supplying insight into the validity of the secular approximation.