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# Re: maximum entropy and the seeking of lowest PE

On Thu, 16 Oct 1997 16:20:33 -0700 Leigh Palmer <palmer@sfu.ca> writes:
I am aware of no such principle. What is usually meant is that the
system
is seeking a state of maximum entropy; and the 2nd Law of
Thermodynamics is
really the basis that should be used to explain phenomena where
"minimization of Potential energy" is often quoted.

The principle is minimization of mechanical energy in mechanical
systems.
The minimization must be accomplished in accord with the laws of
angular
and linear momentum conservation, for example. Without those laws the
Earth would plummet into the Sun because that is a state of much lower
potential energy than the present state. Such a process could not
simul-
taneously conserve angular momentum and finish in a lower rotational
kinetic energy state, however.

Why not a principle of minimization of mechanical energy, Joel? Could
it
not be just another form of the second law of thermodynamics operating
according to the mechanism David described which maximizes the entropy
of the system? There are certainly other statements of the second law
which don't mention entropy at all.

Leigh
****************************************************************************
I can't believe that all these approaches (I mean in phase space - not in
an intellectual sense) to equilibrium are not all part and parcel of the
same thing. Whether they come in variational get-up or dynamic duds,
mechanical or thermodynamic, least or virtual, water runs down hill and
minimal surfaces are modeled by soap bubbles. In an amusing computer
experiment described in P. W. Atkin's *Second Law* for a Mark I universe
consisting of 10,000 square pixels tesselating a square 100 x 100 pixels
each of which is in state "on" or state "off", one can see the approach
to equilibrium coincident with the disappearance of gradients and the
convergence of the Mark I entropy function to its max.

I can't imagine understanding this better cloaked in the specialized
jargon of a distinguished discipline. In science, it is our business to
put things in other words (mo' better words), but I can't imagine what
the incantation would be that could make this plain fact of "life"
clearer.

I will say this: When a description of nature is rendered that seems to
take us closer to the "thing itself", nine times out of ten the subject
is topology. Presumably, someone could write a topological description
of approach to equilibria with many exciting facets.

Dave, I enjoyed your beautiful account of the considerations attendant
upon a large supply of microstates, but I don't think that it is a unique
way of explaining the facts.

I hope my amateur status is not thought to disqualify me from this
discussion. When I look at the vast repository of science and
mathematics on my own shelves, I often regret that I did not dedicate
myself totally to 'cosa nostra', but then I look at my drums, the things
I have built, and the many books outside of science and math, and I am
satisfied. (I am especially satisfied with the writing I have done over
the last ten years after a lifetime of literary pursuits.)

Regards / Tom