Is ergodicity a reasonable hypothesis?
  In the physics literature "ergodicity" is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We also suggest that this feature does not contradict most physical considerations since those considerations deal with correlations of only a few particles. 
Bernard Gaveau and Lawrence S. Schulman
cond-mat.stat-mech physics.chem-ph physics.hist-ph