[Fis] phenomenological entropy

To: <fis@listas.unizar.es>
Subj: phenomenological entropy

Dear FISers,

I would like to to thank Robert for his excellent comments.
(Who said they are idiosyncratic?). Here is Robert's conclusion:
<< So I would conclude with a plea to respect the autonomy of
   thermodynamics from statistical mechanics -- that whatever overlap
   entropy might have with probabilistic notions pales in comparison with
   its meaning in a physical, energetic sense. None of which is to
   diminish the value and utility of Shannon's probabilistic measure,
   which has been enormous. It's just a plea to call it something like
   "uncertainty", "indeterminacy" or even (heaven forbid!) "complexity",
   but at all costs to avoid calling it "entropy"! >>

Yes, for many physicists, STATISTICAL MECHANICS *IS* THERMODYNAMICS,
but for me, STATISTICAL MECHANICS *IS A MODEL FOR* THERMODYNAMICS.
As Robert noticed, thermodybamics has sense at a phenomenological
macroscopic scale. This is quite different from probability calculations
done on a mathematical model. If we have several finite discrete
distributions defined on a model, we have several entropy values from
Shannon formula. Which one is the most adequate for entropy calculation?
The number of microstates is coming soon in the discussion, but I leave
it for next weeks.

Aleks Jakulin noticed also the differences between entropy concepts:
<< Clausius' (thermodynamic) entropy is very different from Shannon's entropy.
   Thermodynamic entropy is a narrow concept. Thermodynamic entropy is
   something one can measure. Shannon's entropy is instead a general one. It is
   a property of a probabilistic model. >>
And:
<< Again, it is very important to distinguish statistical H from the thermodynamical S.
   Some authors use S for Shannon's entropy: very unfortunately, as this is a
   major contribution to confusion.>>

In fact, I am now optimistic about the distinction between entropy concepts.
I am less optimistic about the deep understanding of the phenomenological
thermodynamical entropy, even if its variations are measured in some
situations.

The confusion seems arising from a more general viewpoint:
A physical phenomenon must not be confused with any of its mathematical
models. Many scientists do this kind of confusion, and neither von Neuman
nor Shannon can be involved when the confusion arise in fields other
than thermodynamics. May be after centuries, millenaries, or never,
most physical systems will be fully understood via very complex
mathematical models. But we are far from this (and think to biology
and social sciences!). Modellers have work to do.

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 Wed Apr 14 11:04:34 2004