Poincaré Recurrence Theorem
Abstract
Henri Poincaré showed that if the system has a fixed total energy that restricts its dynamics to bounded subsets of its phaase space, the system will eventually return as closely as someone like to any given initial set of particle positions and velocities. However, one can argue that this kind of recurrences are inconsistent with the second law of thermodynamics. Even though the recurrence time is too large to observe, this theoretical discussions enlightened perspective of mankinds about nature. In this seminar, we will discuss how to prove the theorem in a modern way and apply it to the dynamical systems.
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