On 26.01.2012 12:00 Russell Standish said the following:
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.
Well, I do disregard the surface effects. However, the statement was
that the informational entropy is the same as thermodynamic entropy, so
we must consider the total entropy.
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.
I do not believe that effects below the experimental noise are important
for empirical science. You probably mean then some other science, it
would be good if you define what science you mean.
Evgenii
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