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Re: Entropy: sorted=0 unsorted=237



At 10:02 AM 2/11/00 -0500, Barlow Newbolt wrote:
I can't even
figure out if you are talking about thermodynamic entropy, informational
entropy, or the twilight zone between.

I'm firmly in the "in between" zone. I find it quite well illuminated. I
see no need to distinguish between Carnot entropy and Shannon entropy.

But you ask a good question. For years it was not clear that the two were
the same. But there are good arguments (involving Szilard engines and
such) that indicate they are the same, and I've never seen an argument in
the other direction.

At 10:54 AM 2/11/00 -0500, Barlow Newbolt wrote:
I thought the probability of any particular arrangement of cards in
a deck is the same.

Good! Indeed all such microstates are equally likely.

It shouldn't matter (in my view) whether the cards
are all arranged in order or not--they are in some order and that is all
that matters.

Well, it depends on what you are told about the deck.
--) If you are told it is sorted (in the standard order), then there is
only one ordering that is consistent with that description. That's zero
entropy.
--) In contrast, if you are told that the deck is unsorted, then there are
something like 54 factorial different orderings that are consistent with
that description. That's 237 bits of entropy.

Does that help?