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What Chains Does Liouville’s Theorem Put on Maxwell’s Demon?

Recently Albert and Hemmo and Shenker have argued that, contrary to what is sometimes suggested, Liouville's theorem does not prohibit a Maxwellian demon from operating but merely places certain restrictions on its ability to operate. There are two main claims made in this article. First, that the restrictions Liouville's theorem places on Maxwell's demon's ability to operate depend on which notion of entropy one adopts. Second, that when one operates with the definition of entropy that is usual in this debate, the restrictions put on Maxwell's demon are not even as severe as Albert and Hemmo and Shenker argue.