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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...".
(I should have said "though we don't know which ones these are".)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).
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.