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.
The detailed balance condition in quantum statistical mechanics.Journal of mathematical physics, 25(3):614–616, 1984
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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.