Re: [Phys-L] approach to equilibrium ... not necessarily monotonic

[John Denker <jsd@av8n.com>]

In the context of the hypothesis:

> >   Heat can never spontaneously flow from a lower-temperature 
> >   region to a higher-temperature region.              [1]

and in the context of second sound ....

On 05/31/2012 05:53 PM, Bernard Cleyet wrote:
> Regular sound too?  (first sound)
>
> How about oscillations in and air cylinder with a weighted (massed) piston?

Hmmm.  That's an incisive question.  That requires us to consider
additional hypotheses, namely hypotheses about the definition of
"heat"
 A) heat = energy
 B) heat = random kinetic energy (or random energy in general)
 C) heat = energy accompanied by a large amount of entropy
 D) heat = hotness (as measured by temperature)
 E) heat = energy that moves solely because of a difference in temperature

I was looking for an example that would disprove hypothesis [1].

I reckon that if you choose definition (A), (B), or (D), the example of regular 
sound (i.e. first sound) requires us to either discard hypothesis [1] *or*
choose a different definition of "heat".  That's because the energy does flow
uphill against the temperature gradient during part of the sound-wave cycle.

OTOH I reckon that if you choose definition (C) or (E) then hypothesis [1]
is not invalidated by the example of first sound.  That's because first sound
is isentropic;  the entropy does not flow uphill (or flow at all) during the
sound-wave cycle ... and although the energy moves, it's hard to argue that it
moves solely (or even primarily) because of the difference in temperature.

===

Returning to the other test case, namely second sound:  In this case the
entropy does flow, and it does flow uphill.  Temperature is essentially the
only relevant variable.  Second sound is launched using a heater and detected
using a thermometer.  One could quibble about the definition of "because",
but if energy does not move "because" of temperature in this case, it does
not do so in any other case.

So I conclude that second sound is a stricter test of hypothesis [1].  I do
not see how hypothesis [1] survives, no matter what the definition of "heat".

As I said before:
  It is true that for an ordinary material such as a hot potato, the
  equation of thermal conduction is heavily overdamped, but this must
  be seen as a property of the material, not a fundamental law of nature.