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Re: [Phys-l] Arrow of Time Issue

When we refer to the micro-state of the particles that constitute the coin, what are we looking at? Pauli exclusion reminds us that particles are linked together throughout the universe and that if the quantum state (not energy level (thank you Brian Cox on BBC)) of say an electron shifts, then any electron on the opposite side of the universe will be affected (meaning its quantum state will change). Here is an example of a change in entropy via the subatomic particles shifting as a result of probability. It is outlined in the entropy equation...


Also, Mr. Denker, if you could not link to your personal website (but rather someone else's) to support your conclusions your statements would have more truth to them (although I did enjoy reading your paper on entropy randomness computation in machines, it was very good!).


On Mar 13, 2012, at 10:35 AM, John Denker <jsd@av8n.com> wrote:

In the context of flipping five coins:

On 03/13/2012 04:11 AM, Brian Blais wrote:

"only 32 microstates?" there are more microstates than that,

There is a separation of variables. The heads/tails part of the
system has only 32 microstates. We can understand the microstates
and the entropy of this subsystem separately from the rest of the
system.

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?

Yes and no. It depends on what you mean by "the" system and what
you mean by "the" microstate. Again: We can factor out the
heads/tails subsystem and describe its microstates and its entropy
separately.

Separation of variables works for the entropy whenever the variables
are statistically independent. You can prove that it works, as an
easy corollary of the definition of entropy and the definition of
independent probabilities. The details are worked out at
http://www.av8n.com/physics/thermo/entropy.html#sec-s-independent
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