Liouville theorem states that in a conservative Hamiltonian system, such as a single particle in external electromagnetic field, the phase density of many non-interacting systems is preserved as one follows the motion of the system.

Note that we can apply Liouville's theorem to an ensemble of non-interacting particles, but not to strongly interacting particles. However, if one has a conservative fluid then Liouville's theorem exactly applies. Such case is collection of particles interacting through self-generated electromagnetic fields.

Dusan Maletic