The Recurrence Paradox (Arrow of Time)

The recurrence paradox is something entirely different from reversibility; it is based on an 1890 theoretical result due to the great French mathematician Henri Poincare. Motivated by the question of the stability of the motion of three masses governed by Newton's laws of mechanics (the famous “three body problem”). Poincare showed that under very general conditions any fixed-volume system will return infinitely often and with arbitrarily little error to almost every previous state. If you wait long enough, implies Poincare's theorem, Pearl Harbor will happen again, and again, and again, and. . . . In 1896 the German mathematician Ernst Zermelo used this result (called the “eternal return” by philosophers) to claim that there could be no truly irreversible processes, and thus he cast doubt on the inexorable increase of entropy as really defining the arrow of time.