Re: macroscopic vs microscopic degrees of freedom

[John Denker <jsd@MONMOUTH.COM>]

At 07:16 AM 10/31/99 -0800, John Mallinckrodt wrote:
> On Sun, 31 Oct 1999, John Denker wrote:
>
> > ... In many cases of interest, a qualitative separation of timescales
> > suffices.  Quantifying the timescale is unnecessary.
> >
> > In particular, consider the case of the ordinary block sliding on the
> > ordinary table, which is where I came into this thread.  The thermalization
> > timescale is fantastically short compared to the natural, conventional
> > timescale in the problem (i.e. the duration of the sliding motion).
>
> I believe I might say just the opposite.  The sliding ceases quite
> quickly.

Quickly in what units?  The sliding takes a macroscopic amount of time, for
ordinary blocks on ordinary tables with ordinary initial velocities, using
the ordinary notion of macroscopic.  Can we agree this timescale is at
*least* a tenth of a second?  The thermalization occurs on a much shorter
timescale, as you seem to say yourself a few sentences later.  So except
for this one word "quickly" it seems to me you are saying the *same* thing
I'm saying, not the opposite.

To move the discussion from terminology to physics, let me assert that
(unlike a fluid which has eddies) the block has no internal degrees of
freedom that can store nontrivial amounts of nonthermal energy for
macroscopic time.  If you doubt this, calculate the damping time for
ultrasonic waves in wood or brass.

> The internal energy of the block increases by some definite
> amount during that same period.  Then, over a substantially longer time
> period that depends on the size of the block and its thermal conductivity,
> that nonthermalized internal energy becomes thermalized internal energy in
> keeping with the second law.  (Of course, during that same time scale the
> block is likely to gain or lose internal energy through thermal exchanges
> with its surroundings.)

It doesn't depend on the size of the block quite so much as that.  If it
quickly forms a hot *region* (as you say below) that suffices to justify
everything I've been trying to say.  And I dispute the claim that the
thermalization takes a time substantially longer than the time over which
the energy is gained.  My estimates (based on the stick/buzz model
previously posted) suggest that thermalization should take a microsecond at
most.  If you have another estimate, please be specific about the physical
mechanism that produces your timescale.

> But I have room for and understand the utility of other viewpoints.  I
> understand that you might simply be saying that the frictionally induced
> internal energy is rapidly thermalized in situ creating a "hot" region
> along the bottom of the block with a reasonably well defined temerature
> that is different from the temperature in the rest of the block.

Yes, that's what I'm saying.  Your sympathy for this viewpoint is
reassuring.  In previous email you seemed to disdain the notion of "thermal
energy" but now you seem to be accepting the notion of "hot regions" and
"thermalized" internal energy.  I consider this progress.

> It is
> quite possible to specify reasonable temperatures for different parts of a
> large enough system because thermalization itself takes place on time
> scales that depend on the size of the region you are talking about.

OK.

> > In a finite pond, if the water is macroscopically stationary before
> > paddling and also macroscopically stationary afterward, after the eddies
> > have died out, then I can paddle for hours with no effect other than
> > heating the water.  On my specified timescale, paddling has done no
> > mechanical work at all on the water.  No work.  Just heat.
>
> I understand your viewpoint.

OK.

>  I don't particularly like it because it
> seems to me to confuse "macroscopic forms of internal energy" with "work"
> and "microscopic forms of internal energy" with "heat."

Well, I'm not sure "confuse" is the right verb, but I confess to
considering work to be synonymous with imparting macroscopic forms of
internal energy, and heating to be synonymous with imparting microscopic
forms of internal energy.

> > The distinction between work and heat rests on the notion of entropy.
>
> And I would say that it depends on the notion of "thermalized" versus
> "nonthermalized" internal energy.

Yes.  That sounds like an equivalent statement.

> The conventional
> definition of work is a mechanical *transfer* of energy.  I would call the
> eddies mechanical or nonthermalized forms of internal energy.

My notion of "conventional" work excludes microscopic random energy
transfers.  These are just as "mechanical" as nonrandom transfers *if* you
look super-closely, but still I claim they should be called heat whereas in
a previous posting you seem to say should be classified as work not heat.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com