Re: [math/phys] Equilibrium & Opt., a question for Vu~

[Aiviet Nguyen <aiviet@cat.syr.edu>]

I don't think those are solutions in a strict meaning.
In fact, if physicists want to solve the physical problem of equilibrium
they have to solve the math problem of triangle. However, the heuristic
way of thinking is very important that let us develope the vision across 
the disciplines.

  The equilibrium in terms of energy is not the most general one, however
it is valid for a broad enough class of phenomenae. A litle bit more 
general is so called minimal action principle, where the equilibrium is 
the point or orbit that has an action as a functional to be minimal.
  In terms of math, this is a variation problem that leads to a differential
equation ( s) called Euler-Lagrange.

  Of course there exists more general system that requires more sophisticated
definitions. 

  In a down-to-Earth meaning, equilibrium is a point where a certain gradient
vanishes. 
  
  I was interested in the concept of dynamic equilibrium but failed to 
give a good formulation. The observation starts from a curl on water.
There should be an equilibrium that keeps the shape of the curl stable.
That kind of equilibrium can not be understood in term of the useual 
static way, because the water particles come and go continuously. They 
replace each other but obey the same pattern. They are not tied there as
in mechanical examples.

  This kind of equilibrium is more likely in complex systems like social
and industrial ones.

Cheers
Aiviet