I understand that in Statistical Mechanics Liouville’s equation applies to the probability density of ensembles where microstates’ trajectories are governed by Hamiltonian dynamics. However I’m confused about its application to microstates in the canonical ensemble where microstates can have different energies. If we assume ergodicity, a microstate in the canonical ensemble would visit configurations with different energies and thus its energy would not be conserved along its trajectory. Is ergodicity not applicable to the canonical ensemble or is Liouville’s equation more general and can apply to non-conserving energy trajectories?