From: Osher Doctorow, [log in to unmask], Sat. Sept. 30, 2000, 10:29PM
Nantana Naranong has also requested information on Gibbs' inequality. I
don't do that every day, or I probably could say it in a few intuitive words
(in fact, that's one of my conjectures - mathematicians/statisticians and
scientists who do things everyday can express them in a few intuitive words
if they (a) really want to, (b) are good enough at words. There might be
(c) are paid enough, but that would eliminate not only the "free world"
(whatever that is) but the whole world, so I won't press the point now. One
of my favorite references for summarizing Gibbs' work (other than the
original Gibbs papers) isWalter T. Grandy, Jr. Foundations of Statistical
Mechanics, Volume I, Equilibrium Theory, Reidel: Dordrecht, 1987. It should
be read together with A. Dembo and O. Zeitouni Large Deviations Techniques
and Applications, Springer: New York, 1998, for a modern treatment which
ties it in with one of the 10-15 top research areas in
mathematics/statistics, namely, large deviations (which really is part of
rare events including tail events).
Having said all this, I will have to go back to those works, which I have,
and reread them, before I can say much more profound. Let me qualify that -
I understand rare events, but Gibbs is about as rare as they become. I
somebody else finds out first, I will graciously bow to him/her and bite my
tongue.
Your Friend in the Grand Canonical Assembly [this is some of Gibbs and
Boltzmann's terminology - you can see that this is not going to be easy]
Osher Doctorow
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