Well, trivially, a dynamical system with that switches between two states is ergodic. We always know what the past state of the system was given the present. N

Well, trivially, a dynamical system with that switches between two states is ergodic. We always know what the past state of the system was given the present. No, ergodicity is more about visiting the each part of the phase space with some positive frequency i.e. on a long trajectory you see everything that can happen, and not too infrequently.