For real ergodicity it is necessary that your system goes through all points of your phase space (at least through the ones which are energetic accesable).

However, you can have certain systems that are quasi ergodic. This means that the trajectories of your particles can come abitrarily close to every accessably point in your phase space.

I am not sure what you mean by "glassy systems" - if you mean spin glasses or phase transitions then ergodicity may be violated due to the formation of new subsets in your phase space which are disjoint.

Disjoint means that they have no points in common, but each of them may be ergodic within itself.

Thus particle may be able to reach each point in one of these subsets, but it may not be able to reach all points in the next one - so a subset might be ergodic but not the whole phase space.

H Johannes,Thanks for your answer.

Yes by glassy I mean something similar to spin-glass system.

Here, another question rises: Can we define entropy for the so-called quasi ergodic systems, in the same fashion that it is defined for ergodic systems (considering that the system can not actually reach all its accessible states)? In other words, for calculating the entropy, should we take into account all of the accessible states, or just the ones that system is kinetically able to pass through them?

Thanks.

Entropy is per definition (at least if you consider the definition of Boltzmann - there are other definitions as well) a measure of the part of your phase space, which can be reached by your particles, if your observables (V, T, N) are conserved.

Hence I don't think that you can have an entropy for non-ergodic systems.

Thanks Johannes.