From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Trouble at the 0K corral!
Keywords: WE ARE IN TROUBLE FOLKS!!!!!!
Organization: Department of Chemistry, University of Toronto
Distribution: bionet
Date: Thu, 12 Nov 1992 02:40:37 GMT

In article <BxKoJw.9Mr@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider)
writes:
>In article <1992Nov11.212802.16407@alchemy.chem.utoronto.ca>
>mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>|     I don't think that an imperfect crystal can ever be described as
>|having a temperature of 0K.  With every type of imperfection I can
>|imagine (even isotopic heterogeneities) there has to be an associated
>|energy term.
>
>Perhaps you could give a few examples of what you imagined?  Where does
>that energy term come from?

     Take the case of isotopic heterogeneities.  There are various
complicated nuclear forces which give one nucleus a higher energy than
another.  The nuclei are weakly coupled (through the electroweak current
or, if you believe in such things, through some sort of GUT force) both
to each other and to the electrons, so even if the electrons have all relaxed
to their lowest energy state (and thus have an effective temperature of
0), you can't describe this system as having a temperature of 0K (or
even as being in a state of equilibrium) since the "nuclear state"
temperature (which is coupled to the other degrees of freedom as
described above) is non-zero.
     Let's take something more familiar, namely lattice imperfections.
The lattice energy has electron-electron, electron-nucleus and
nucleus-nucleus terms.  One can think of dislocations, vacancies and other such
imperfections as regions of high energy.  (One ocasionally reads the
term "dislocation energy" although one should take it with a small grain
of salt, at least.)  In principle, if one waits long enough, these
dislocations will anneal out.  (This is an activated kinetic process.
How long one has to wait depends on the temperature, although not in the
usual Arrhenius way because of tunneling.)  They therefore represent a
nonequilibrated degree of freedom.
     In my opinion, we are lead to such (admittedly) silly examples by
poking too hard at the least well-understood and perhaps least
fundamental of the laws of thermodynamics.  It's fun to think about, but
I'm not convinced that we are likely to learn any physics this way.

>|This suggests that
>|you in fact can't freeze in imperfections in the manner we have all been
>|discussing.
>
>This seems to make sense except for one thing:  I thought that 0K was
>defined.  So here you are drawing a conclusion about what nature can
>do based on a definition!

     At any temperature above 0K, nothing is really frozen.  We have
just slowed all rates to the point where it looks frozen on the time
scale of the experiment.  Since the third law (or a corollary thereof)
states that you can't get to 0K, I am certainly not drawing conclusions about
nature from a definition.  Rather, I think that I was in the above
passage pointing out some of the logical peculiarities of our
definitions and postulates.  I couched my argument in experimental terms
because that's the language I'm most familiar with, but I didn't mean to
imply that I thought that I was discussing an actually realizable
experiment.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca