  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
unitary system propagator. Employing spectral analysis we prove the general
form of the ensuing master equation. We compare this result to master equations
obtained from standard microscopic derivations. The obtained formal structure
can be employed to test the compatibility of approximate derivations with
thermodynamics. For example, it designates that global master equations are the
compatible choice. The axiomatic approach sheds light on the validity of the
secular approximation in microscopic derivations, the form of the steady state
in heat transport phenomena, and indicates the lack of exceptional points in
the dynamics of open quantum systems.
