On 25.01.2012 21:25 meekerdb said the following:
On 1/25/2012 11:47 AM, 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?

The thermodynamic entropy is a measure of the information required to
 locate the possible states of the plates in the phase space of
atomic configurations constituting them. Note that the thermodynamic
entropy you quote is really the *change* in entropy per degree at the
given temperature. It's a measure of how much more phase space
becomes available to the atomic states when the internal energy is
increased. More available phase space means more uncertainty of the
exact actual state and hence more information entropy. This
information is enormous compared to the "01" stamped on the plate,
the shape of the plate or any other aspects that we would normally
use to convey information. It would only be in case we cooled the
plate to near absolute zero and then tried to encode information in
its microscopic vibrational states that the thermodynamic and the
encoded information entropy would become similar.

I would say that from your answer it follows that engineering information has nothing to do with the thermodynamic entropy. Don't you agree?

It would certainly interesting to consider what happens when we decrease the temperature (in the limit to zero Kelvin). According to the Third Law the entropy will be zero then. What do you think, can we save less information on a copper plate at low temperatures as compared with higher temperatures? Or more?


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