Chapter 9: Fundamental Physics

Section 3: Irreversibility and the Second Law of Thermodynamics

Poincaré recurrence

Systems of limited size that contain only discrete elements inevitably repeat their evolution after a sufficiently long time (see page 258). In 1890 Henri Poincaré established the somewhat less obvious fact that even continuous systems also always eventually get at least arbitrarily close to repeating themselves. This discovery led to some confusion in early interpretations of the Second Law, but the huge length of time involved in a Poincaré recurrence makes it completely irrelevant in practice.

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From Stephen Wolfram: A New Kind of Science [citation]