Sbharris[atsign]ix.netcom.com wrote:

These maximally-fast entropy-generating systems which self-evolve in a
non-equilibrium system through which energy is running, and in which
things are free to mechanically move around and adjust themselves to
entropy transport, are called "dissipative structures" by Prigogine.
Prigogine got the Nobel prize I think because everyone was under the
impression that he's mathematically explained the evolution of these
things.

:-)))

That's a priceless sentence. :-)

But I don't think he did.

Sbharris[atsign]ix.netcom.com wrote:

These maximally-fast entropy-generating systems which self-evolve in a
non-equilibrium system through which energy is running, and in which
things are free to mechanically move around and adjust themselves to
entropy transport, are called "dissipative structures" by Prigogine.
Prigogine got the Nobel prize I think because everyone was under the
impression that he's mathematically explained the evolution of these
things.

:-)))

That's a priceless sentence. :-)

But I don't think he did. There's some controversy about
whether or not Prigogine's theories explain (in a fundamental
mathematical sense) any real-world phenomenon that chemists or
physicists before him, couldn't. Sure enough, these things form, as you
noticed! But alas, I don't think anybody to this day knows generally
WHY they do. So you're onto a deep mystery, all right.

Well, now that it's OK for me to express doubt, I did wonder just how
much that paper you referenced explained. But then, as we know, I
don't understand it, so I have to give them the benefit of the doubt.

(Hmm... I wonder it that's actually a realistic precept. There will
always be arcane things one does not follow, and a certain percentage
of these one will have to judge bunk/non-bunk on probability. And
that's how Sokol was born).

I think they assert they have reproduced the migration of the bead to
points of resonant tuning ... but if the "force" I questioned in my
other post is really defined to drive the system up the "kinetic energy
gradient", that would be a necessary result, wouldn't it? In other
words, if you know the end state, and define a "force" to get you
there, you will necessarily reach the expected end state.

Perhaps the answer could be as simple(?) as that the resonant
configurations are actually max entropy configurations under the
driving constraints -- forget "second order entropy -- i.e. , after one
is convinced that plain old entropy can be sufficiently well defined
for an open system. IOW, given any point in phase space near the
resonance, there would be many more ways for the system to fall into it
than to fall out of it -- the usual entropic story.

In fact, in very broad terms, that must be true. How else could the
system evolve? The open "non-equilibrium" constraints are merely
unusual from the point of view of elementary thermo. Nature doesn't
know if we've only formalized elementary thermo, though. She merely is
going to go for maximum probability under the constraints.

I don't know what kind of esteam Prigogine is still held in, among
thermodynamicists. If any. Cognoscenti say his name with two hard g's,
if that's any help at cocktail parties where the origin of
irreversitiliby is being debated.

Thanks. Now I am saved from that gaffe, should the occasion ever
arise. :-)

http://cscs.umich.edu/~crshalizi/notebooks/prigogine.html

SBH