I am trying to understand the concept of ergodicity/ergodic system in physics, but because my understanding of phase space, its elements is a bit unclear,I have trouble understanding the former. Regarding ergodicity (in physics), in Wikipedia I read this:
A physical system is said to be ergodic if any representative point of the system eventually comes to visit the entire volume of the system.
A point in phase space, represents a microstate as far as I understand. Also in the case of MCE or CE the microstates are eigenstates of the hamiltonian. That doesn't mean that it can't also be a superposition of the eigenstates of the Hamiltonian (please correct me if my understanding is faulty here). Now if a point (system) gets to visit the entire volume of the system, doesn't that imply that the microstate changes its energy, and isn't that in contradiction to the Liouville theorem where we say that the change of a system is governed by the Hamiltonian mechanics?
Edit: What does it mean for a system to spend time in a region of phase space?