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reading the very interesting discussion on the long thread on the 2nd law, had a couple of much more basic questions regarding entropy & the Poincaré Recurrence Theorem
A) is the reduction of entropy implied by the theorem a real, unresolved paradox in physics?
B) if you take a frictionless pool table and a system that begins with a break, the recurrence theorem would state that eventually the system will go back to the point where the balls are racked with the cue ball traveling toward them at the original momentum. how would you quantify the reduction in entropy of this state, if any?
Is maximum entropy achieved when all the balls on the table have the same momentum / kinetic energy?
this seems odd since at random there would be elastic collisions where all the momentum of one ball was transferred to another, leaving the first ball at rest. this happening to all but the cue ball where the balls are re-racked seems unlikely though.
A) is the reduction of entropy implied by the theorem a real, unresolved paradox in physics?
B) if you take a frictionless pool table and a system that begins with a break, the recurrence theorem would state that eventually the system will go back to the point where the balls are racked with the cue ball traveling toward them at the original momentum. how would you quantify the reduction in entropy of this state, if any?
Is maximum entropy achieved when all the balls on the table have the same momentum / kinetic energy?
this seems odd since at random there would be elastic collisions where all the momentum of one ball was transferred to another, leaving the first ball at rest. this happening to all but the cue ball where the balls are re-racked seems unlikely though.