On 1/27/2012 12:43 PM, Evgenii Rudnyi wrote:
On 27.01.2012 21:22 meekerdb said the following:
On 1/27/2012 11:21 AM, Evgenii Rudnyi wrote:
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?

Obviously not since I wrote above that the thermodynamic entropy is a
 measure of how much information it would take to locate the exact
state within the phase space allowed by the thermodynamic
parameters.

Does this what engineers use when they develop communication devices?



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?

Are you being deliberately obtuse? Information encoded in the shape
of the plate is not accounted for in the thermodynamic tables - they
are just based on ideal bulk material (ignoring boundaries).

I am just trying to understand the meaning of the term information that you use. I would say that there is the thermodynamic entropy and then the Shannon information entropy. The Shannon has developed a theory to help engineers to deal with communication (I believe that you have also recently a similar statement). Yet, in my view when we talk about communication devices and mechatronics, the information that engineers are interested in has nothing to do with the thermodynamic entropy. Do you agree or disagree with that? If you disagree, could you please give an example from engineering where engineers do employ the thermodynamic entropy as the estimate of information.

I already said I disagreed. You are confusing two different things. Because structural engineers don't employ the theory of interatomic forces it doesn't follow that interactomic forces have nothing to do with sturctural properties.

Brent


My example would be Millipede

http://en.wikipedia.org/wiki/Millipede_memory

I am pretty sure that when IBM engineers develop it, they do not employ the thermodynamic entropy to estimate its information capabilities. Also, the increase of temperature would be destroy saved information there.

Well, I might be deliberately obtuse indeed. Yet with the only goal to reach a clear definition of what the information is. Right now I would say that there is information in engineering and in physics and they are different. The first I roughly understand and the second not.

Evgenii



Brent



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