Re: [Fis] Re: Only One Entropy

On Mon, 3 May 2004, Michel Petitjean wrote:

> About the "unique" entropy":
>
> ... Here again, I consider that the system and its model are two
> different entities. It is why, in some practical situations dealing with
> entropy, I consider that the informational entropy is able to modelize
> the physical entropy, but IS NOT the physical entropy. If the two
> entropies are the same, informational entropy has at least to work in
> all situations where thermodynamical entropy is measured. This is
> difficult to believe. And what about the converse ? I cannot see
> thermodynamics in all fields in which informational entropy is used.

Perhaps it would be helpful here to point out that statistical "entropy"
is defined in abstraction from all conditions in which it could be
applied. The Boltzmann formulation describes a physical system. It
consists not only of the formula, but ALSO of the "boundary value"
specifications. That is, physical entropy does not exist in abstraction
from physical constraints in which it is embedded. (Michel wrote earlier
in his posting of symmetry, for example.)

Anyone who has played with statistical "entropy" knows that it can rise OR
FALL, depending on the circumstances under which it is being applied. Not
so the Boltzmann entropy. It can only rise because of the physical
constraints (extra "baggage" I like to call them :), which are usually not
mentioned in most discussions comparing the two measures.

So in my own mind, it takes both the Boltzmann formula AND it attendant
baggage to model physical entropy, whereas the statistical indeterminacy
(a term I much prefer to "entropy") is unencumbered by a specific set of
baggage and can be applied to circumstances that do not mimic physical
entropy. (You can perhaps detect that I travel only reluctantly. :)

Physicists tell us that a full problem specification consists of the
description of the field equations and their attendant boundary
constraints. All too often in biology we focus solely upon the field
dynamics and ignore the accompanying boundary conditions. Neo-Darwinists,
for example, are quick to wield Occam's Razor in praise of their very
simple "field description" and against those who might suggest more
complex formulations. But they notably fail to mention that their "natural
selection" poses a boundary condition of virtually infinite complexity.
The possibility exists that through a slightly more complex dynamics that
internalizes some of the selection, the accompanying boundary
specifications are more than proportionately simplified. The revised
formulation could be simpler in toto; i.e., it is conceivable that the
neo-Darwinian description falls on the very sword it's proponents are so
keen to use against others.

I will now step down from my soapbox! :)

The best to all,
Bob

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Robert E. Ulanowicz | Tel: (410) 326-7266
Chesapeake Biological Laboratory | FAX: (410) 326-7378
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1 Williams Street | Web <http://www.cbl.umces.edu/~ulan>
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Received on Mon May 3 16:04:01 2004