Geodesic
Detailed Balance, Time Reversal, and Generators of Quantum Markov Semigroups
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 108-116

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We characterize generators $\mathscr L$ of norm continuous quantum Markov semigroups satisfying the quantum detailed balance condition with respect to an antiunitary time reversal in terms of the operators $H$ and $L_k$ in the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) representation $\mathscr L(x)=i[H,x]-(1/2)\sum_k(L^*_kL_kx -2L^*_kxL_k+xL^*_kL_k)$.
Keywords: quantum detailed balance, time reversal, quantum Markov semigroup, Lindblad representation, antiunitary operator. 
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     author = {F. Fagnola and V. Umanita},
     title = {Detailed {Balance,} {Time} {Reversal,} and {Generators} of {Quantum} {Markov} {Semigroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {108--116},
     publisher = {mathdoc},
     volume = {84},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a7/}
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F. Fagnola; V. Umanita. Detailed Balance, Time Reversal, and Generators of Quantum Markov Semigroups. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 108-116. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a7/