Since the times of Ludwig Boltzmann, most physicists take it for granted that generic non-integrable closed dynamical systems, whether classical or quantum, thermalize at long times for generic initial conditions. Whether this belief is true or false depends on the type of systems one is willing to consider and the meaning of “generic” and “thermalizes”. In this talk I will discuss two types of many-body dynamical systems where thermalization (i.e. weak convergence to the state of maximal entropy) can be established for a large class of initial states. The first one is a system of an infinite number of spins with evolution generated by a repeated application of a Clifford Cellular Automaton. The second one is the classical counterpart of the first one and can be thought of as a mixing automorphism of an infinite-dimensional torus.