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Re: [Phys-l] the uniqueness of entropy



From: WC Maddox

With regard to the second paragraph below from previous message: The
authors quoted below argue that the mechanism that moves the partition in
and out in the situation described in the articles cannot be ignored in the
statistical mechanics case even though it is ignored in the thermodynamics
case in all 3 articles.
They undercut their own argument by saying that one can define a
"reduced (statistical) entropy" that include the N! term so the value from
thermodynamics agrees with statistical mechanics value. They say "there is
nothing wrong with the reduced entropy if it is interpreted from this
pragmatic point of view. "

Note: The different views are not limited to the authors of the two AJP
articles. Swendsen's AJP article starts with a list of different views he
has found among physicists about entropy. It would have helped if Boltzmann
had not contributed two formulae that give different numerical values.
Perhaps someone on Phys-L with strong opinions on the subject could
contribute a third article to the AJP or at least a letter to the editor.

The IAU sometimes decides arguments based on definitions for astronomers
(Pluto is/is not a planet). Perhaps the APS, or on the international scale,
the International Union of Pure and Applied Physics could serve a similar
function for physics. It looks like the IUPAP book called Symbols, Units,
Nomenclature and Fundamental Constants in Physics was last issued in 1987.
Perhaps it is time for an update including an appendix on the topic of
dueling definitions.

End Message

On 06/30/2011 06:28 AM, William Maddox wrote:
Not everyone agrees with 2a even within physics. The authors of
the paper on entropy in the July issue of AJP, who are disagree with
Swendsen's Journal of Statistical Physics article, state: " The key to
the resolution is the recognition that the entropy concept in
thermodynamics is not identical to that in statistical mechanics".

In particular, in the context of re-inserting the partition in a Gibbs-type
mixing experiment, the quoted claim that
"According to statistical physics, there is a decrease of W
and thus of the entropy."
is just wrong. That's not what the statistics (or the physics) says. It's
just not true classically, quantum mechanically, mathematically, or
otherwise.