For finite-dimensional quantum Markovian semigroups, the standard quantum detailed balance condition is equivalent to a special generator representation that yields vanishing entropy production under thermodynamic consistency.
Entropy production for quantum dynamical semigroups.Journal of Mathe- matical Physics, 19(5):1227–1230
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Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production
For finite-dimensional quantum Markovian semigroups, the standard quantum detailed balance condition is equivalent to a special generator representation that yields vanishing entropy production under thermodynamic consistency.