Global Evolution of Entropy
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.
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