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Re: [Phys-l] Arrow of Time Issue



On Mar 9, 2012, at 16:39 PM, John Denker wrote:

Messiness (aka disorder) should not be equated with entropy.

For the next level of detail, see
http://www.av8n.com/physics/thermo/entropy.html#sec-s-vs-disorder


I went back an re-read some of this, and had a peculiar thought.

I got to the point where you describe one of the problems with the tidy/messy room: "Even if we stipulate that the tidy state is unique, we still don’t know whether a shirt on the floor “here” is different from a shirt on the floor “there”. Since we don’t know how many different disorderly states there are, we can’t quantify the entropy."

and then read the next example:

"Perhaps the simplest example is five coins in a closed shoebox. Randomize the coins by shaking. The entropy at this point is five bits. If you open the box and peek at the coins, the entropy goes to zero. This makes it clear that entropy is a property of the ensemble, not a property of the microstate. Peeking does not change the disorder. Peeking does not change the microstate. However, it can (and usually does) change the entropy. This example has the pedagogical advantage that it is small enough that the entire microstate-space can be explicitly displayed; there are only 32 = 2^5 microstates."

and I thought, "only 32 microstates?" there are more microstates than that, I thought. and then I considered that I guess we don't really know in this example whether a coin on the floor of the box "here" is different from the coin on the floor of the box "there", so we don't know how many different disorderly states there are. perhaps the number of states is somehow proportional to the surface area of the floor of the box? of course I realized that you were only referring to the heads/tails part of the state, but the position of the coin in the box is also part of the microstate, yes?


bb


--
Brian Blais
bblais@bryant.edu
http://web.bryant.edu/~bblais
http://brianblais.wordpress.com/