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



On 05/31/2012 08:50 AM, William Maddox wrote:
Is Phys-L down again?

I've been monitoring the server. My records indicate that it has
been available /at least/ 99% of the time over the last week.

=======================

And now for some actual physics. Consider the following assertion:

Heat can never spontaneously flow from a lower-temperature
region to a higher-temperature region.

I've seen lots of authorities who either "postulate" that this is
the second law of thermodynamics, or "prove" that it is equivalent
to the second law of thermodynamics.

I don't buy it. In addition to various minor counterexamples, I can
think of at least one major counterexample, namely _second sound_ in
superfluid helium. The temperature oscillates.

In general, there is no law that says the approach to equilibrium must
be monotonic. As a simple example, consider an underdamped harmonic
oscillator. Both the position and the momentum oscillate on their way
toward equilibrium.

In general, some variables approach equilibrium monotonically, while
others do not.

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.

For details on all this, including diagrams, see
http://www.av8n.com/physics/thermo/spontaneous.html#sec-approach-equilibrium