Global Evolution of Entropy

Abstract

In Chapter 3 we have shown that invertible systems have absolutely constant entropy, namely H _c (P ^t f | f _*) = H _c (f | f _*) for all times t (Theorem 3.2), while for noninvertible systems the entropy may increase (Theorem 3.1) since H _c (P ^t f | f _*) ≥ H _c (f | f _*). Thus, noninvertibility is absolutely necessary (though not necessarily sufficient) for the entropy of any system to increase from its initial value.