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## Main Question or Discussion Point

**Challenging Susskind's "uncompressible flow" in Liouville’s Theorem**

It’s in Susskind’s 7th lection on the classical mechanics when he’s approaching Liouville’s Theorem he’s using "uncompressible flow" term to express the idea that divergence of flow in phase space is 0 – as much of flow is entering a volume the same amount of flow is leaving the volume. The idea is very simple but I didn’t understand why he called the flow "uncompressible” and based his explanation on "uncompressibility” of the flow. Now I know (please correct me if I’m wrong here) that by "uncompressible flow" he meant exactly div=0 but I feel that "uncompressible” and “div=0” do not follow one from another.

1) It’s obvious that in some places of the phase space lines with the same H will go closer to each other than in other places what is exactly “compression” in my book (but div=0).

2) Even compressible flows can have div=0. Imaging a cube volume with a flow going into it from 5 sides with some speed v and going out of the volume from 6th side with the same speed v but compressed 5 times denser – div still will be 0 despite it’s compressible flow.

Please help me understand whether "uncompressible flow" was a poor choice of words or "uncompressibility" is really related to div=0 (at least for Liouville’s Theorem).

Thank you.