Isothermal Maxwell daemon: numerical results in a simplified model

A recently suggested simple model of an open microscopic system interacting with a bath and behaving like an isothermal Maxwell daemon is simplified and treated numerically. Results obtained confirm expectations that the system can, at the cost of thermal energy of the bath, spontaneously and in a cyclic process, pump particles from a particle reservoir to states with even higher energy. This contradicts the usual opinion based on the second law of macroscopic thermodynamics. For this effect, the interaction with the bath cannot be treated as weak. The role of dephasing owing to this interaction is illustrated.