Entropy of the Universe

In which Fernando asks a question, and CIP gets confused.

In some ways the initial Universe, which is hot and uniform would seem to have a high entropy. Of course we have good reason to believe that the entropy has been increasing, at least since the big bang. If we stick to classical thermodynamics, the entropy change of a system undergoing a reversible change is given by dS = Q/T, where dS is the entropy change, Q the heat transferred, and T the temperature. So for an isolated system, undergoing reversible change, the entropy can't change. You might think that our universe is an isolated system, but it isn't really. Because our Universe is expanding at an accelerating rate, stuff at the boundaries of the Universe keeps "falling off the edge", that is going beyond the observable horizon. Another kind of horizon exists around black holes, so the amount of matter in the observable U keeps shrinking. On the other hand, dark energy keeps increasing.

Any smart person want to explain to me how all this affects the entropy?

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