[Fis] Re: miscellanea / temperature / symmetry

To: <fis@listas.unizar.es>
Subj: [Fis] Re: miscellanea / temperature / symmetry

Dear FISers;

Pedro asked a very imprtant question: what are the relationships
between temperature and entropy.
I heard about temperature first as a function of pressure and volume
for gas (equation of state). Then, going further in thermodynamics,
came thermal equilibrium, heat, thermal exchanges, Carnot engine and
Carnot cycle. It appears that the definition of temperature and
the definition of entropy arise both here, and are closely intricated
(e.g. see the first part of the book of Alberty and Silbey).
Temperature is related to energy in gas kinetic theory.
I do not go further because we are now disconnected from "information",
but I do the following remark:
Ask to people what is temperature and what is entropy: most will
claim that they know what is temperature, but little people will
claim that they know what is entropy, although both concepts
are defined within the same course of thermodynamics.
(imagine what would think people if temperatures and entropy values
appeared together on the TV screen, when the wheather is commented...).

About symmetry and its relations to entropy: symmetry theory and
entropy (information theory) are both related to distributions.
But, symmetry theory has to work for distributions, discarding whether
they are finite discrete, or infinite, or continuous. Informational
entropy is mainly connected to finite discrete distributions, despite
some extensions in the continuous case.
Much more problematic is that the entropy associated to a discrete
distribution does not care of the numerical values to which non null
probabilities are attached, and in fact, entropy exists even if the
probabilities are defined on a non numerical space: e.g.:
P(red)=1/3, P(green)=1/3, P(blue)=1/3 is a distribution for which
entropy can be calculated. This is false for symmetry calculations,
which deals mainly with euclidean multivariate distributions.
So, entropy and symmetry are quite different. An other question
is their relations with order and disorder...

This is my 4th message for this week. I will be silent until next week.

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 Thu Apr 22 11:02:25 2004