[Phys-L] Re: entropy: increased by stirring, decreased by observation

[John Denker <jsd@AV8N.COM>]

On 06/12/05 15:11, Bob Sciamanda wrote:
> | The crucial contribution to the entropy is
> | _not knowing_ where the particles are. If you know where
> | they are, it doesn't matter whether they are mixed or
> | not ...
>
> Suppose John knows where all of the particles are, but Mary doesn't know
> where any of the particles are.  What is the system's entropy?

1) As a matter of principle, the two observers
will assign two different values to "the" entropy.

_Human_ observers are so grossly dissipative and
usually "know" so little that it is academic to
worry about the thermodynamics of _human_ "knowledge".

However, the issue takes on new life when we
consider highly-optimized robot measuring devices
-- Maxwell demons and the like.

2) For microscopic systems, it is for sure possible
for one observer to know enough to change the entropy
by a significant percentage.

By way of analogy, you know that different observers
report different values of "the" kinetic energy
(depending on the velocity of the observer), and
this hasn't caused the world to end.

3) For macroscopic systems (10^23 particles or
thereabouts) it is uncommon for one observer
to know 10^23 things that the other observer
doesn't ... but even this is possible.  The spin
echo experiment is a celebrated example.

4) Regardless of the size of the system, it is often
illuminating to consider a complete thermodynamic
_cycle_, such that all participants are returned to
the same state at the end of the cycle.

This de-emphasizes what the observers "know" and
instead focuses attention on how they "learn", or (in
less-colorful language) on the observation/measurement
process, which is reeeally important if you want a
deep understanding of what entropy is and where it
comes from.

In particular, the observer who "learns" more about
the system will dissipate more energy during the
process of making measurements on the system, by an
amount that scales like temperature * entropy.
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