2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228661The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition mechanisms, and their role for relative entropy dynamics is discussed.19 pagesQuantum Physicstext