Re: [Phys-l] the uniqueness of entropy

[John Denker <jsd@av8n.com>]

On 06/29/2011 08:42 AM, William Maddox wrote:
> Any opinions on this: In his Journal of Statistical Physics article is
> Svendsen supporting a "one size (formula) fits all" view ("by defining the
> entropy as the log of the probability distribution. both classical and
> quantum statistical mechanics can- be treated consistently.") or is he
> limiting the inclusion of N! in the entropy formula to ideal gases
> ("Different experimental conditions produce different expressions for the
> entropy)?


Some things are negotiable, and some things are not.

1a) In science, there is only one definition of energy.

1b) Outside of science, there are many nontechnical and metaphorical
 definitions of "energy", but this does not change fact (1a).

1c) Any possibility of multiple kinds of energy would defeat the
 purpose of the first law (i.e. conservation of energy) and would
 make a mockery of the laws of physics.

1d) There are of course innumerable corollaries of the basic laws,
 applicable in various more-or-less restricted situations.

2a) In science, there is only one definition of entropy.

2b) Outside of science, there are many nontechnical and metaphorical
 definitions of "entropy", but this does not change fact (2a).

2c) Any possibility of multiple kinds of entropy would defeat the
 purpose of the second law (i.e. paraconservation of entropy) and 
 would make a mockery of the laws of physics.

2d) There are, again, innumerable corollaries of the basic laws,
 applicable in various more-or-less restricted situations.


3a) All the above stands in contrast to other terms such as "heat"
 and "adiabatic" which even within physics have multiple incompatible
 definitions ... with little hope that any single definition will
 prevail over the others any time soon.

3b) The ill-definedness of "heat" in item (3a) is not a problem, precisely
 because of items (1a) and (2a).  For serious work, people don't try to
 quantify the heat, but rather quantify the energy and entropy.

> ("Different experimental conditions produce different expressions for the
> entropy)?

It depends on what you mean by "expressions".  Different conditions lead
to different corollaries and consequences ... not to different definitions
or principles.