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Re: [Phys-l] riddle : entropy



1) S/N = (log_2(3) - 2/3) bits = 0.918295834 bits
where N = # members in the ensemble

2) S/N = (P_A*log_2(1/P_A) + P_B*log_2(1/P_B)) bits
Substitution of P_A = 1/3 & P_B = 2/3 into the above formula
yields the result 1) above.

Which are the "Lots of 'authoritative' references will lead you
to the wrong answer"? Maybe I'm missing something, but I don't
see what is supposed to be so puzzling here. It seems pretty
straightforward to me with nothing subtle or tricky in the problem.

David Bowman

________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of John Denker
Sent: Fri 3/23/2007 12:03 AM
To: Forum for Physics Educators
Subject: [Phys-l] riddle : entropy



Here's a seemingly-simple puzzle:

Suppose we have a system that can be in either of two
microstates. Actually we have an ensemble of such
systems, and repeated measurements have observed the
system to be in microstate "A" with probability 1/3rd
and microstate "B" with probability 2/3rds.

Two questions:

1) What is the entropy of the system?

2) How sure are you that your answer is correct?

Hint: It's easy to get the right answer, but it's also easy to
get the wrong answer, depending on how you approach the problem.
Lots of "authoritative" references will lead you to the wrong
answer.

The usual jsd puzzle rules apply: Everything I've said here is
true and helpful, to the best of my knowledge. But obviously
I haven't told you everything; for instance I haven't told
you the answer. This isn't a word game; solving the puzzle
requires understanding the physics, not quibbling about words.
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