Re: Entropy question

Zigoteau wrote: 
Hi Andy,



I don't think that's what I'm saying.  Although, to be truthful, I'm not
sure what you mean by "normal" mechanics. Newtonian? Continuum? Quantum?




Well, at the current time quantum is the gold standard, but you use the
others, which can be derived as approximations to QFT, when you've got
to solve a problem in the time available.

 All have their advantages and disadvantages, and (partially
overlapping) spheres of applicability.



But they have a hierarchy of validity.

I'm not sure I buy that. I'll go along with Newtonian mechanics (i.e. the dynamics of mass-points) is an approzximation of QFT. But continuum mechanics seems to be a different animal altogether. At least as I understand it, based on Truesdell and Noll's writings. The concepts are different, the continuum theory has a more complete mathematical foundation than even quantum mechanics- continuum mechanics has been axiomatized, quantum mechanics has not (again, AFAIK).

I resist using the term "hierarchy", as it implies that lower-level theories are somhow closer to some sort of ultimate truth, and that higher-level theories are "coarse-grained" approximations to lower-level theories. Certainly, Newtonian mechanics can be translated into quantum mechanics fairly easily. I have seen no such tratement of continuum mechanics: constitutive relations, for example. Where is the quantum treatment of the stress-strain relationship? Cauchy's law? Or even a quantum mechanical version of stress and strain? I'm not claiming they don't exist, just that I have not seen one.


<snip> 

I don't think that's true at all- contact line motion cannot currently
be explained by mechanics.




What have you got against the Blake theory? I think that the fit to it
is quite reasonable, all things considered. I think that it might be
possible to get a better theory by taking account of the
2-dimensionality of surfaces: Blake's theory is essentially
one-dimensional. However enlightenment has not yet arrived in this
particular brain.

I am unfamiliar with the Blake theory- do you have a reference? The only work I have seen is by E.B. Dussan V. and her collaborators. In Slattery's book "Interfacial Transport Phenomena", he clearly and plainly states that no complete solutions exist for moving and deforming phase interfaces (p. 923).


Chemi-osmotic processes (Peter Mitchell's
Nobel winning theory on cellular respiration) cannot be explained by
mechanics,


Of course they can. They involve pumping protons and other ions across
insulating membranes against a voltage gradient. Totally mechanical.

nor can any chemical-mechanical system like muscles. "Heat"
can't be explained in terms of mechanics.




Of course it can. What do you think statistical thermodynamics is all
about? In the first ten pages of their textbook, Landau and Lifshitz
derive from fairly general concepts of equilibrium that the probability
of a state of a system with energy E is proportional to exp(-E/kT). You
can then write down the internal energy U = (1/Z) Sum E.exp(-E/kT)
where Z = Sum exp(-E/kT). If you move from one condition to another,
the change of U is not all accounted for by mechanical work: energy
must have been put in in another form: the difference dQ is heat. It is
easy to show that the quantity dQ/T is integrable: entropy S. Next, the
simplest expression for a thermodynamic quantity is F = U-TS = kTln(Z),
from which you can derive all the others. Thence all of classical
thermodynamics. A doddle.

Ok, let me back up. Maybe I misunderstand what you mean by 'mechanics'. I may be able to write down a potential energy U which has contributions from gravity, electromagnetism, chemical potentials, enthalpy, etc. etc., and from that write down a force [-grad(U)], but this 'force' is qualitatively different from a Newtonian 'force': at what spacetime point does the force resulting from an unbalanced chemical reaction act?. So we say we are dealing with "generalized" forces: it looks like a force, but it isn't a *force*.... maybe it acts in some abstract phase space or something. That's fine and ok, but it's no longer properly mechanics.

Especially so, a large part of *mechanics* is concerned with dynamical behavior, but thermodynamics and statistical mechanics (at least the way you use it above) is solely concerned with *equilibrium*. Even the statistical mechanics of steady state is way more complicated: see volume 10 of L&L.

<snip>

I wonder if we are getting off track here: my thesis is that "statistical mechanics" contains concepts not derivable from mechanics- concepts that cannot be considered as an approximation to the dynamics of mass-points. Or of the deformation of continous media. Or of quantum fields. Also, I'm not claiming that statistical mechanics is in some way more fundamental than mechanics.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.