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