tangent off of Order being born from disorder?

["Michael N. Monce" <mnmon@conncoll.edu>]

On Mon, 19 May 1997, Leigh Palmer wrote:


-snipped

> The entropy has been shown to be a measure of uncertainty, indeed, and I'm
> pleased to see David using that term in preference to the odious "disorder".
> It is, however, a measure of uncertainty at *all* scales of length, not only
> the submicroscopic. Uncertainty is also related to timescale, by the way, a
> fact both David and I have swept under the rug to this point. The
> uncertainty in the order of a pack of cards is zero once it has been
> isolated from a source of shuffling; that is why the entropy contribution
> due to any particualr order is the same: zero. In the limit of incredibly
> long times one could fancifully imagine that cards could change places, say
> by quantum mechanical tunneling, and that would increase the "uncertainty".
> The order of an initially arranged pack would be as uncertain as that of an
> initially shuffled pack, however; the entropy increase due to consideration
> on an incredibly long time scale would be the same for both cases (and
> negligible compared to other terms, including the amplitude of the expected
> entropy fluctuations).
-snipped

	These comments by Leigh raise a related issue that I've had
trouble understanding.  Hawking, and others, state that the directionality
of time is related to entropy; something I don't quite grasp.  When Leigh
says 'long timescales' is this referring to time's directionality?  If
the uncertainty was not related to timescale, would there be a
directionality?  

	I tried taking Leigh's example of a deck of cards: Imagine a
universe that consisted of just a deck of cards and a mechanical shuffler
that only shuffled when, say, a radioactive decay occurred within the
mechanism; sort of a Schrodinger's cat type machine.  In between shuffles
when the deck's mechanism is idle, is there a directionality to time,
since nothing is contributing to the entropy? 

	I've got lots of questions here, but no answers.


					Mike Monce
					Connecticut College