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.