Reference https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/“Knowledge and Entropy are properties of the system and the state of the system (and possibly external factors too). Information is a property of the system and independent of the state.[iv]”
My understanding of Liouvilles Theorem is that it deals with a conserved "density" defined on phase space, not with the concept of "volume" alone. Perhaps "phase space" in physics has definition that involves this density in addition to the ordinary mathematical concept of "volume"?Even better, Liouville’s Theorem[viii] says that if we choose a region in phase space (see D above); it evolves in time to different positions and shapes, but it conserves the volume in phase hyperspace.