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If Liouville’s theorem states that an area in phase space doesn't change, then can the area go scattered, but with total area conserved? If not, wouldn't it be contradicted to the entropy law?

Qmechanic
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Shing
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    Are you asking whether the support of the phase space distribution function can become split into different connected components and whether this tells against the second law? Also, to confirm, you mean the hypervolume, rather than area, right? Only in one dimensional systems (2D phase space) is the hypervolume given by an area. – Selene Routley Jun 18 '17 at 10:44
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    Or are you asking how can entropy increase if Liouville's theorem say it doesn't change? If so, then the question suggested by @valerio92 would seem a very good fit. – Selene Routley Jun 18 '17 at 10:45
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    @WetSavannaAnimalakaRodVance basely yes, I was thinking how Liouville’s theorem not violate the second law, then the only way out I saw was: it would scatter into connected "complicated" shape gradually. – Shing Jun 18 '17 at 13:00

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