Second law of thermodynamics for random walk of quantum particle in a presence of detectors

We test H-theorem for a several models of particle random walk. We study interaction with a reservoir/detectors and its influence on entropy and found entropy growing in the time for some models and behaving non-monotonically for the others. We discuss the details of the system-reservoir interaction (such as presence of the interference in the system and number of interactions with detector parts) and their impact on the monotonicity of entropy.