Understanding the phase-space representation of Ensembles

[Harry Mason]

Hello , i have some troubles with basics concepts of statistical mechanics.
I feel confortable with the general idea of an Ensamble, a collection of copies of the physical system which differs from each other due to microscopic differences and having the same macroscopic behavior.

I'm ok also with the concept that a point in a 6N-dimensional phase-space represent a specific microstate of the system itselt but i fell unconfortable with the idea of 'motion' of these points.

I see the ensemble as a 'cloud' of non-interactive points each of them representing a particular allowed state.
Why should these points follow trajectories? According to the hamilton equations the possible solution are all the microstate and at a fixed energy , possible microstate are fixed so I can't imagine any motion in this space.

 

[Harry Mason]

I think I wrote it in the wrong section.
I mean, maybe the 'Atomic, solid state anch comp. physics' section should be better, but I don't know how to move the post.