About Liouville's theorem(classical mechanics)

[kof9595995]

Here is a statement about the Liouville's theorem in my textbook:
"Because we are unable to discuss the details of the particles' motion in the actual system, we substitute a discussion of an ensemble of equivalent systems. Each representative in the phase space corresponds to a single system of the ensemble, and the motion of a particular point represents the independent motion of that system"
I don't understand what it means by "independent" in the last sentence, does it mean the particles are assumed not to collide with each other in the real configuration space?

 

[dx]

Independent here means that the different systems in the ensemble have nothing to do with each other. The time evolution of a system in the ensemble depends only on its starting point in the phase space (and the Hamiltonian).

 

[kof9595995]

Independent here means that the different systems in the ensemble have nothing to do with each other. The time evolution of a system in the ensemble depends only on its starting point in the phase space (and the Hamiltonian).

So "Independent" includes the collisionless case I mentioned, or such as particles don't exert force on each other, am I correct?