2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228662The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.34 pagesMathematical Physics60J10; 81Q99text