From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Newsgroups: bionet.info-theory
Subject: Re: Question on entropy at 0K
Keywords: Pinheads PseudoScience FlameThrowers Reality-check
Date: 12 Nov 92 17:45:50 GMT
Distribution: bionet
Organization: Department of Chemistry, University of Toronto

In article <1992Nov12.092326.29496@ncsu.edu> samodena@csemail.cropsci.ncsu.edu
(S. A. Modena) writes:
>Equilibrium calculations are special
>cases of the general theory.  When you talk about "extending"
>equilibrium state calculations to cover non-equilibrium, aren't you
>in serious trouble?

     In one sense, yes.  What I was pointing out was that we had a
perfectly satisfactory theory of thermostatics (the inaptly named
"classical thermodynamics") but no proper theory of nonequilibrium
behaviour.  (Actually, that's not quite true either.  We have an excellent
understanding of steady-state behaviour as well.  Of course, by an
appropriate change of coordinates, you can always turn a steady-state
process into an equilibrium one.)  Ideally, we would have a theory of
nonequilibrium thermodynamics from which we would infer equilibrium
properties.  We're simply not there yet.
     To put this discussion in a historical context, our situation with
respect to thermodynamics is essentially that of the ancient Greeks with
respect to mechanics:  They understood statics quite well but did not
have any coherent theory of dynamics.  (We can debate the role of
Aristotle in classical Greek physics if you like.)

>Rewmember, I'm a non-mathematician and non-physicist.  From
>Newton onward, the Universe operated by Newtonian Mechanics. But,
>Einstein corrected that misconception, didn't he? Did he do it
>by EXTENDING equilibrium macro-mechanics to cover the Relativistic
>Universe?  Is Quantum Mechanics an EXTENSION of Newtonian Mechanics?

     I would say yes, on both counts.  Then again, I've been brainwashed
that way.  In a more serious vein, I would say that special relativity
is definitely an extension of classical mechanics.  It introduces no
truly new concepts to mechanics, although it modifies several.  The
epistemological status of Q.M. is more problematic.  I really wouldn't
know how to place G.R. in this discussion either.

>Is Statistical Mechanics an EXTENSION of Newtonian Mechanics.

     There is a sense in which statistical mechanics is both more and
less revolutionary that any of the other theories mentioned above.  On
the one hand, it "just" builds on mechanics (either classical or quantum).
On the other hand, it introduces new and somewhat revolutionary
concepts; the whole business of ensembles really has no clear connection
to classical particle mechanics and only a fuzzy one to quantum
mechanics.
     
>I'll admit to being an ignoramus.  

     I will similarly admit that parts of this discussion are quite far
out of my area of expertise.

>Define ZERO Kelvin.

     Absolute zero is the temperature at which a system is in its lowest
attainable energy state.  The debate centres around the word
"attainable".  In experimental situations, we only worry about what is
attainable in the lifetime of the experiment.  In such a case, there
might very well be imperfections remaining near 0K which we can consider
to be frozen in.  However, on a sufficiently long time scale, there
will certainly be lower attainable energy states (non-thermalized
degrees of freedom) for any ordinary experimentally realizable system.
(For related comments, see McClare's J. Theor. Biol. paper on
thermodynamics.  I can supply a precise reference on request.)
     In a sense, we are getting into trouble because we are doing this
backward.  Personally, I like the so-called "Rational Thermodynamics"
way of treating these problems.  (See Truesdell's book for details.)
Let's not pretend that we don't know what temperature is.  Temperature
is what you measure with a properly conceived thermometer.  At low
temperatures, gases make good thermometers and 0K is defined by the
vanishing of the product PV.  The third law is simply the observation
that (as Peter pointed out) for almost every process, d(Delta G)/dT
vanishes as the ideal gas temperature goes to zero.  From this and the
handful of counterexamples we have to this rule, we can gain some
insight into the nature of entropy.  When we try to push things further
than this, we are forced to ask awkward questions so let's admit that we
haven't yet solved all the problems of thermodynamics and just keep
those awkward questions in the backs of our minds in the meantime.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: bionet.info-theory