[XorNot]

I'm going to need an example on the differences, because in so far as statistical entropy is entropy - it's ultimately describing an information function (and the lean in quantum mechanics these days is that information is describing physical properties as well - hence holography and the blackhole information paradox).

The heat-deathed universe for example would be the ultimate compressible information: 1 measurable state, across all space, for the rest of infinite time.