Does the Poincaré recurrence theorem violate entropy (second law of thermodynamics)?
he Recurrence theorem apparently contradicts the Second law of thermodynamics, which says that large dynamical systems evolve irreversibly towards the state with higher entropy, so that if one starts with a low-entropy state, the system will never return to it. There are many possible ways to resolve this paradox, but none of them is universally accepted.[citation needed] The most typical argument is that for thermodynamical systems like an ideal gas in a box, recurrence time is so large that for all practical purposes it is infinite. However this explanation is not entirely satisfactory, since there is not, in fact, any characteristic timescale in the system, compared to which the recurrence time could be said to be very large.
