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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...".

That is the criterion for attainment of what is called "thermodynamic
equilibrium". There is an identifiable time associated with any system's
tenure in a single microstate (a single cell in phase space). The time
required to reach the remotest cell in the phase space under given set
of constraints is the equilibration time. Of course the system does not
have to attain that particular microstate; it is enough that it is, in
principle, accessible from the initial state.

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?

Two things. Thermodynamics does not apply to small systems; it was
never meant to. The other is that the evolution of a small system
is not predicted by the quantum mechanics. The billiard game in Mr.
Tompkins is a nice example of that.

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.

To understand the conclusion you must accept the premise. Acceptance
of the premise is your conceptual block. Let me approach this in a
different way. I have before me a thermodynamic system. I know enough
about it to be able to compute the entropy of this system. You, on
the other hand, know nothing about the system,and there fore you
cannot calculate its entropy. Do you not believe that the system has
a perfectly definite entropy even though you are ignorant of it?

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.

There's no blame. Entropy is more easily understood if extraneous
noise about "disorder" and "information" are not introduced. The
problems start when the student makes an effort to subsume these
ideas into the concept from the beginning. Start with understanding
reversible processes in macroscopic systems. (These are all ideal.)
When you understand what is meant by the statement "The entropy of a
thermodynamic system is a function of its state" you will be well on
the road to understanding the concept. As it stands you now do not
believe that statement, and progress is very difficult in consequence.

Leigh