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Re: Entropy, Objectivity, and Timescales



Leigh says...

What one can say is that the
interactions of the parts of the system are of such a nature that the
microstate changes during the time period in question in such a manner
that in principle it *could have* reached any of the states which are
considered to be in the set of accessible states. It is not necessary
that the system reach even 10^-10 (or any small fraction) of them.

I'm sorry, I'm afraid I don't understand what is meant by "in principle
it could have...". What information am I allowed to use in order to
determine which states "could have" been reached? For instance, consider
a system of just two helium atoms. If all I tell you is that they're
confined to a box of a certain size and have a certain total energy,
you'll conclude that all sorts of states are accessible. If I add the
information that one atom is currently at rest and the other is moving
more or less toward it with a certain speed, you'll still conclude that
quite a few states are accessible after they've had time to collide.
But if I then add the information that the aim is bad and they're going
to miss, you'll come up with a much smaller number of "accessible"
states (for the short term).

(If you don't like an example with just two particles, I'll ask you
to specify the minimum number of particles needed before we're allowed
to talk about entropy.)

It seems to me, therefore, that entropy is fundamentally a *subjective*
quantity, a measure of our ignorance.

Here you must immediately see the fault in your logic.

No, I'm afraid I don't.

Mere use of
the word "therefore" does not cover the holes in your argument. Is
there an argument, by the way?

No comment.

If I knew the precise microstate
of the helium now, then I could predict its microstate at all times
in the future for the next billion years, and even counting every state
that it explores as "accessible" I'd get an entropy much less than the
generally agreed upon value. The agreed upon value, though, includes
an enormous number of other microstates that the helium will never
actually explore (though we don't know this).
(I should have said "though we don't know which ones these are".)

You don't know (and you can't know) the exact microstate of any
physical system, and it is fundamentally impossible to predict even
its microstate after the next transition, let alone in the distant
future.

Not true. For a sufficiently small system I can know the precise
microstate, and I can predict its state into the future using the
Schrodinger equation (or Newton's laws for a classical system).
I don't know of any fundamental limitations for larger systems--
only practical limitations. Am I missing something?

The entropy of a system is not a subjective quantity. Now that you
understand that you also understand why the entropy associated with
the order of the cards in the deck is zero.

Sorry, I still don't understand either.

It seems that this post is an example of a misconception that can
result from the association of an established, well understood
physical concept like entropy with something that is formally similar
(the "Shannon entropy" as Dave Bowman calls it) but physically
unrelated.

I'm not very well read on these technicalities. I'm just trying to
make sense of the concept of entropy in the best way I can. So if
I'm totally wrong, I take full responsibility, with no blame
whatsoever on Shannon or anyone else.

Dan