On 1/9/2014 2:26 PM, Jesse Mazer wrote:

Liouville's theorem is derived in deterministic classical mechanics. If you take avolume of phase space, each point in that volume is a specific microstate, and if youevolve each microstate forward for some time T using the deterministic equations ofphysics, you get a later set of microstates which occupy their own volume in phasespace. Liouville's theorem just says the two volumes must be equal. It only becomesstatistical if you interpret the original set of microstates as representing your ownuncertainty--if you just know the original macrostate, you may choose to consider thestatistical ensemble of microstates compatible with that macrostate, then they will givethe "volume of phase space" that you start with. But that's just an extra layer ofinterpretation, Liouville's theorem itself is not really statistical.

`Right. And entropy, the log of the number of possible states, only increases when`

`"possible states" is defined by some macroscopic constraint. There is always a finer`

`microstate definition of possible states such that the number and the entropy don't`

`increase. Entropy is a consequence of coarse-graining.`

Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.