Re: [Fis] definition(s) of order/disorder ?

Dear Michel and colleagues,

Before attempting a response to the 'order/disorder' theme you have
proposed us, let me terminate the speculations on entropy/temperature I
started last days. Actually both reflections might be quite close, as the
proposal to leave aside the 'entropy as disorder' interpretation should
imply efforts both on a new proposal about entropy interpretation, and on
the clarification of the order/disorder theme (several authors in this list
could make valuable contributions to the latter, I think particularly in
Karl's logical "distinctions" and neighborhood relationships, based on set
theory; and also in Michael Leyton approach to symmetry breaking by
symmetry extension out from group theory; in Gyuri's approach, Loet's, etc.
And of course, some of 'complexity science' approaches to order/disorder,
e.g., based on Kolmogorov's algorithmic randomness).

To continue, How that 'extensivity' of energy carriers measured by entropy
might be interpreted beyond disorder? A naive response from a biology
aficionado may be that if Temperature informs us about the average energy
per individual degree of freedom (1/2 Kb.T), then what entropy measures is
some sort of 'space-time increase' regarding the whole (molecular) degrees
of freedom. Depending always on the boundary conditions (as Stan implied),
the input of energy into our molecular system, will cause an increase
either in the spatial extension, or in the velocity distributions, or in
both. The molecular system, by definition, has zero entropy at 0 K, then as
energy is entered into the system it will start to increase its spreading,
its motions (translation, rotations, vibrations) and so to increase its
space-time occupancy, its degrees of freedom. Energy gets always
"equipartitioned" among the different degrees of freedom (the three
translational dimensions, plus rotations and vibrations --as was much
discussed for multi-atomic gasses, and as was also stated for solids by the
equipartion Law of Dulong and Petit).

A global metric of such increase in the degrees of freedom is given by the
entropy calculation ---that can be approximated in terms of statistical
mechanics and in refinements related to the famous Bolzmann-Planck formula.
But we may also need to enter within that global quantity that measures the
entropy increase or decrease in molecular states. In my view, this is what
Shu-Kun attempts in his analysis of the molecular similarity cases; and
traditionally physical chemists have used a lot symmetry and group theory
tools for tabulating the approximations to'real' entropy changes that
contribute to Gibbs' free energies of chemical reactions.

So, entropy increase would indicate (and measure globally) the dynamic
'sponging', the 'dispersion', the 'spreading' of matter in space-time as
energy is added to our system. Although I have encapsulated Frank Lambert
along most of these views, now rather then following him in his choice of
the 'spreading' term as an alternative to disorder, I would prefer either
"space-time dilatation" or 'space-time expansion' of matter.

To add to these naive physical heresies of mine, let me suggest that having
two 'laws' in classical thermodynamics should not deter us in the quest for
a unified principle. Regarding tentative axiomatizations of 'information
physics' (for instance, as hinted in previous fis sessions by Igor and
Shu-Kun), we could consider a return to the initial 'transformation'
meaning of entropy by Clausius. Then a single "principle of
transformability" could take care both of energy conservation and entropy
increase in the transformations we operate or observe in material systems.
Together with another two arch-principles such us uncertainty and
relativity, these three fundamental principles of information physics would
tell any observer about the inevitable information constraints to abide by
along his/her 'motor operations' within nature.

Thanking your patience,

Pedro

PS. When I mention 'motricity' (or motor operations) I really mean that the
natural sciences, particularly physics, have implied a very strong social
commitment to epistemic reliance on the motor part of our whole
"motor/perception cycle": numbering, measurement, dimensions, magnitudes,
'facts', methods, operationalization, standardization, etc. etc. Just for
fun, let us note that a similar social reliance on shared motricity seems
to occur in realms of life situated worlds apart: rhythms, dancing,
drum-beating, marching, parading, exercising, sporting, cheering,
applauding... we adore groupal motricity performed at a unison!

_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis
Received on Wed Apr 28 13:36:26 2004