[FIS] Re: Probabalistic Entropy

To: <fis@listas.unizar.es>
Subj: [FIS] Re: Probabalistic Entropy

Dear FISers,

Here, I would like to reply to Michael Devereux.
I agree that Shannon's entropy is quite general, because it can be
applied to many models of physical systems not necessarily related
to thermodynamics. Shannon's formula is derived from probability
theory, outside any physical field of application, even if it is in the
framework of information theory, which is itself rather a model for
some other phenomenon. Now, thermodynamical entropy S is defined
via the Carnot cycle, and it is a state function of a thermodynamical
system: this latter cannot be confused with a probabilty distribution.
Various mathematical models using or not Shannon's formulation may be
proposed to relate theory and experiments, but the thermodynamical
definition of entropy remains, and has been introduced outside any
probability consideration. Shannon's entropy does not generalizes
thermodynamical entropy. They may be related in a limited number
of situations. One is of mathematical nature, the other is of
physical nature.
The existence of the state function S was in fact postulated
(a quite strange entity), and its variations may be measured.
But observations are less or more precise, although the mathematical
models are just tools: data are input, calculations are made, results
are output. In science, is there any example of calculation without
input data ? So, the <<precision of the model>> is judged from the
departure of <<predicted>> from <<observed>>, the <<predicted>>
being also depending on the precision of the input data, which
are measured data. If physicists are able to output theoretical values
of some measured value on the sole basis on all mathematical axioms and
theorems, please let me know. E.g. could a mathematical proof be built
one day to show the physical dimensionality of our space must be three ?
There are mathematical theories leading to space structures obviously
not compatible with what is observed. An algorithm selecting the
theory adequate for our universe is currently unthinkable: so,
experimental data ARE at the basis of science.

Michel Petitjean Email: petitjean@itodys.jussieu.fr
Editor-in-Chief of Entropy entropy@mdpi.org
ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
1 rue Guy de la Brosse Phone: +33 (0)1 44 27 48 57
75005 Paris, France. FAX : +33 (0)1 44 27 68 14
http://www.mdpi.net http://www.mdpi.org
http://petitjeanmichel.free.fr/itoweb.petitjean.html
http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html
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Received on Fri Apr 16 12:28:06 2004