  Kramers' degeneracy theorem underpins many interesting effects in quantum
systems with time-reversal symmetry. We show that the generator of dynamics for
Markovian open fermionic systems can exhibit an analogous degeneracy, protected
by a combination of time-reversal symmetry and the microreversibility (detailed
balance) property of systems at thermal equilibrium -- the degeneracy is lifted
if either condition is not met. We provide simple examples of this phenomenon
and show that the degeneracy is reflected in the single-particle Green's
functions. Furthermore, we show that certain experimental signatures of
topological edge modes in open many-body systems can be protected by
microreversibility in the same way. Our results highlight the importance of
detailed balance in characterizing open topological matter.
