recurrence theorem in a sentence

1. Related to the concept of eternal return is the Poincar?recurrence theorem in mathematics.
2. British physicist violation of the Second Law of Thermodynamics, one of them due to the Poincar?recurrence theorem.
3. The concept of a wandering set is in a sense dual to the ideas expressed in the Poincar?recurrence theorem.
4. Over an infinite time, there would be a spontaneous entropy " decrease " via the Poincar?recurrence theorem, thermal fluctuations, and Fluctuation theorem.
5. The first result in this direction is the Poincar?recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set.
6. It's difficult to find recurrence theorem in a sentence.
7. These papers included the Poincar?recurrence theorem, which states that certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state.
8. For example, any system for which the Poincar?recurrence theorem holds cannot have, by definition, a wandering set of positive measure; and is thus an example of a conservative system.
9. In particular, I was interested to know how the Poincar?recurrence theorem was consistent with the heat death of the universe ( a consequence of the second law of thermodynamics ) . talk ) 18 : 18, 21 July 2012 ( UTC)
10. It says " The first result in this direction is the Poincar?recurrence theorem " .-- Poincar?_ recurrence _ theorem explains that it was published by Henri _ Poincar?in 1890 . talk ) 14 : 15, 1 June 2012 ( UTC)