On Wed, Jan 25, 2012 at 08:47:03PM +0100, Evgenii Rudnyi wrote:
> Let me suggest a very simple case to understand better what you are
> saying. Let us consider a string "10" for simplicity. Let us
> consider the next cases. I will cite first the thermodynamic
> properties of Ag and Al from CODATA tables (we will need them)
> S ° (298.15 K)
> J K-1 mol-1
> Ag  cr  42.55 ą 0.20
> Al  cr  28.30 ą 0.10
> In J K-1 cm-3 it will be
> Ag  cr  42.55/107.87*10.49 = 4.14
> Al  cr  28.30/26.98*2.7 = 2.83
> 1) An abstract string "10" as the abstract book above.
> 2) Let us make now an aluminum plate (a page) with "10" hammered on
> it (as on a coin) of the total volume 10 cm^3. The thermodynamic
> entropy is then 28.3 J/K.
> 3) Let us make now a silver plate (a page) with "10" hammered on it
> (as on a coin) of the total volume 10 cm^3. The thermodynamic
> entropy is then 41.4 J/K.
> 4) We can easily make another aluminum plate (scaling all dimensions
> from 2) to the total volume of 100 cm^3. Then the thermodynamic
> entropy is 283 J/K.
> Now we have four different combinations to represent a string "10"
> and the thermodynamic entropy is different. If we take the statement
> literally then the information must be different in all four cases
> and defined uniquely as the thermodynamic entropy is already there.
> Yet in my view this makes little sense.
> Could you please comment on this four cases?

Brent commented quite aptly on these cases in another post. The fact
that you calculate the thermodynamic entropy the way you do implies
you are disregarding the information contained in the symbols embossed
on the coin.

If you included these two bits, the thermodynamic entropy is two bits
less, = 4.15 x 10^{-24} J/K less 

This is so many orders of magnitude less than the entropy due to the
material, its probably not worth including, but it is there.


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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