A model of nonautonomous dynamics driven by repeated harmonic interaction

We consider an exactly solvable model of nonautonomous $W^*$-dynamics driven by repeated harmonic interaction. The dynamics is Hamiltonian and quasifree. Because of inelastic interaction in the large-time limit, it leads to relaxation of initial states to steady states. We derive the explicit entropy production rate accompanying this relaxation. We also study the evolution of different subsystems to elucidate their eventual correlations and convergence to equilibriums. In conclusion, we prove that the $W^*$-dynamics manifests a universal stationary behavior in a short-time interaction limit.