Re: [Fis] Distribution of Energy is (not) the same as disorder

Jerry asked:
>Dear Michel, Stan, Loet and all:
>
-snip-

>Stan, can you provide precedence for the usage of the term "dispersion" in
>this context?
>How is the term "dispersion" related to the empirical phenomenon of interest?
>In particular, what sort of narrative can you construct that links
>dispersion to other thermodynamic variables?
>Further, since the distribution of heat energy within a molecule is an
>accurate narrative for the empirical spectral evidence, can you propose a
>stronger narrative for relating the concept of dispersion (scattering) to
>empirical spectral evidence?
>
-snip-

>As pointed out above in my response to Stan, the narrative is rather
>precise when applied to atomic and molecular phenomenon.
>

     SS: Taking the questions seriatim:
>Stan, can you provide precedence for the usage of the term "dispersion" in
>this context?
     SS: The concept of dispersion derives from statistics, where it
signifies wider distribution. In the context of thermodynamics discourse,
it was brought in by Boltzmann in his microscopic model of entropy
increase, the idea being that when energy gradients disperse so that less
energy availability can be derived from them, that is what is meant by
entropy having increased (or, in a more local interpretation, free energy
having decreased). Furthermore, and importantly, the tendency for energy
gradients to disperse is taken (in fact modeled) as being spontaneous
inasmuch as greater dispersion is held to be a more likely configuration
than lesser dispersion in a world where things tend to fall apart (that is,
in a world that is far from thermodynamic equilibrium).

>How is the term "dispersion" related to the empirical phenomenon of interest?
     SS: Dispersion relates to loss of ability to do work as an energy
gradient gets dissipated. The idea is that, in order to afford work, an
energy gradient needs to be focused upon some job to be done. Ths is
better accomplished when the gradient is compact.

>In particular, what sort of narrative can you construct that links
>dispersion to other thermodynamic variables?
     SS: The major concept of import here is thermodynamic potential, AKA
(in our activity-oriented culture) potential for doing work. The more
dispersed an energy gradient is relative to an energy consumer, the less
net work can be done while dissipating it. As for temperature, it
signifies a potential for doing work, which declines as a system cools (as
when warm air expands). The same for pressure.

>Further, since the distribution of heat energy within a molecule is an
>accurate narrative for the empirical spectral evidence, can you propose a
>stronger narrative for relating the concept of dispersion (scattering) to
>empirical spectral evidence?
     SS: Here, I'm afraid I am not knowledgeable enough in the details.
Consulting Brooks III et al, Science 293: 612-613 (2001) on the naturation
of a protein via folding, we find that free energy increases as folding
continues. Conformational entropy is at the same time lost as the parts of
the protein get increasingly fixed in place. This is clearly NOT a
spontaneous process. So, here the free energy is instituted in the folds
of the protein. This energy is less dispersed than it would be if it had
instead been jiggling the protein strands in the unfolded condition. In
this case, the unfolded form has a more distributed energy configuration,
while the native form has its energies less distributed AND less dispersed
-- and would be a greater energy gradient for some (microscopic) consumer
would be than the unfolded condition.

STAN

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Received on Mon Sep 20 01:57:28 2004