>when the universe is just a uniform heat - it won't take much information to describe.
Actually this is when it takes maximum information to describe, as no particle is correlated with any other (and thus no savings from encoding). You basically have to fully describe each particle individually as a point in space. The alternate extreme is where matter is maximally compact and thus maximally correlated.
That's a great way of putting it. Maximum entropy means minimal intrinsic information (and thus you need a lot of external information) and vice versa.
Actually this is when it takes maximum information to describe, as no particle is correlated with any other (and thus no savings from encoding). You basically have to fully describe each particle individually as a point in space. The alternate extreme is where matter is maximally compact and thus maximally correlated.