If information is conserved and the universe is finite, it's also cyclic, and the entropy law is false.
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Very interesting. That does assume that information is always physical, though. But if so, it means that either the universe is not finite or the 2nd Law is false.
"Information is conserved" in this context just means that the laws of physics are deterministic and irreversible (which they are). (See Lecture 1 of Susskind & Hrabovsky, "The Theoretical Minimum".)
