Nonequilibrium phase transitions in feedback-controlled three-dimensional particle dynamics

We consider point particles moving inside spherical urns connected by cylindrical channels whose axes both lie along the horizontal direction. The microscopic dynamics differ from that of standard 3D billiards because of a kind of Maxwell's demon that mimics clogging in one of the two channels, when the number of particles flowing through it exceeds a fixed threshold. Nonequilibrium phase transitions, measured by an order parameter, arise. The coexistence of different phases and their stability, as well as the linear relationship between driving forces and currents, typical of the linear regime of irreversible thermodynamics, are obtained analytically within the proposed kinetic theory framework, and are confirmed with remarkable accuracy by numerical simulations. This purely deterministic dynamical system describes a kind of experimentally realizable Maxwell's demon, that may unveil strategies to obtain mass separation and stationary currents in a conservative particle model.