It seems to me that macrostates should take very few bits to specify (e.g. temperature and pressure), compared to microstates within a macrostate (positions of each molecule). So there would still be a difference overall.
Equilibrium macrostates (such as the homogeneous soup at the end of the universe) can be described using very few macroscopic predicates. Non-equilibrium low-entropy states cannot. No need to go back all the way to the beginning of the universe; just look at the present macrostate. No need to look at the entire universe even, just look at the room you're in. The amount of information you'd need to specify to pick out the current macroscopic state of your room out of all the other macroscopic states of similar entropy it could be in is in fact quite high. A...
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