On 01/17/2012 08:45 AM, Folkerts, Timothy J wrote:
Hmmm ... more to think about.
Yeah. It may take a couple of days to noodle this one out.
Here's a status report on my thinking: I'm sticking with the
proposition that thermodynamic equilibrium is isothermal. I'd
be willing to bet large amounts of money on that.
HOWEVER ... at the moment I don't have a clear explanation of
what (if anything) is wrong with the other way of looking at
things. One of the rules for doing science is to consider *all*
of the plausible theories and check them against *all* of the
evidence. I've tried but not yet succeeded in this case. In
other words, there is something going on here I don't understand.
Here's another angle that may help: Consider the famous Einstein
relation between the mobility (for a particle drifting under the
influence of a force) and the diffusion constant (diffusing under
the influence of a density gradient). This is (a) elegant and (b)
widely used, so I reckon that if there were something wrong with
it, we would have heard about it before now. This is pretty much
the same physics as the original question, if we consider self-
diffusion (rather than the diffusion of a foreign particle, such
as the proverbial Brownian pollen grain). This is another vote
in favor of plain old righteous thermodynamics, apple pie, and
motherhood.
Here's where I intend to go next: All the cases I understand are
in the /hydrodynamic limit/ where there are many many particles
in every parcel of fluid, and the mean free path is short compared
to any other length scale(s) in the problem. It may be that we
are getting fooled by a breakdown in the hydrodynamic approximation.
That is waaaay more plausible than a breakdown in the basic laws
of thermodynamics.
Another possibility is that there is something in the statement
of the original question that tricks us into looking at a non-
equilibrium situation, in some less-than-obvious way.