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Re: Entropy, Objectivity, and Timescales



* I put deeper in quotes because I don't mean to claim that it is 'better'
in any particular way.

It isn't better, and it isn't deeper. Its depth is illusory. You think
it is deeper because it is conceptually more difficult to grasp. Is
that a great virtue that somehow sets it above classical thermodynamics?

What statistical mechanics does is to implement thoroughly understood
classical thermodynamics on the microscopic level. It gives us
algorithms for calculating thermodynamic functions for microscopically
described systems, such as those studied by quantum chemists and
condensed matter theorists. Their systems are described in terms of
sets of orthogonal wave functions which are solutions of Schrodinger's
equation for weird and wonderful hamiltonians. (I hesitate to mention
this, but the hamiltonians are frequently for isolated simple systems.
The interactions which make the thermodynamics relevant are swept under
the rug, that is left out of the hamiltonian, and replaced by the
phrase "weakly interacting".) In order to connect these systems to the
world as we perceive it macroscopically the theorist must calculate
macroscopic properties of his system. He know that he should whomp up
a partition function (according to a well- tested algorithm) and then
apply some rules to calculate those macroscopic quantities.
Thermodynamics *per se* has absolutely nothing to tell the theorist
about his system on a microscopic level. Quantum mechanics must
already have done its best, and that I hope we all agree is something
that QM can't do completely. In particular QM can't help us with
meaning on a microscopic level.

Can we agree that temperature is a macroscopic parameter? How does one
interpret temperature microscopically? It can't be done, despite the
problem in a 35 year old Halliday and Resnick which asks the student
to calculate the temperature of a 10 eV electron. (I don't remember for
sure that it was H&R, but that's what we were using 30 years ago when
the problem was pointed out to me.) Do you think it will be possible to
gain a "deeper" understanding of thermodynamics when one has to
introduce a macroscopic parameter arbitrarily to make the connection?
Where does the Boltzmann factor fall out of QM? I missed that item in
my undergraduate education.

Leigh

Note: The interpretation of temperature in special and general
relativity is an area of controversy. Diverse opinions exist suggesting
that the temperature of a moving system as observed by a stationary
observer is greater than or less than that observed by a comoving
observer. The method of observation of temperature of a moving system
is one which should get your inventive juices going. I opt for optical
pyrometry, but some object to this method. After applying correction
for Doppler shift one will see that a moving system appears to be cooler
than would be reported by a comoving observer.