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*From*: John Denker <jsd@av8n.com>*Date*: Wed, 05 Aug 2009 18:09:00 -0700

On 08/04/2009 09:03 AM, Donald Smith wrote:

.... Ultimately, I agree with the other posters -- you're applying

macroscopic concepts like pressure, temperature and volume to a

system where they don't apply. Hence, the paradoxes.

Excellent. This is what they call "taking the game to the next level".

The levels here are:

1) Expert level: mastery of the subject matter:

2) Instructor level: All of level 1, plus mastery of the pedagogical

and psychological issues.

When we start asking where the paradoxes come from, we are clearly

at the instructional level. After all, there are no paradoxes in

the real laws of physics; paradoxes only arise if/when we

misunderstand the laws of physics.

As previously mentioned, there is a magnificent discussion of

fluctuations in Feynman volume I chapter 46 ("Ratchet and Pawl").

I reckon there are several ideas that need to be clarified:

-- Temperature is not the same as energy density. Suppose

we have a 500 psi bottle of compressed air and also a 1000

psi bottle, both at 300K, both standard size. The latter

has quite a bit more energy (and energy density).

-- Any finite system will exhibit fluctuations, even at

equilibrium. The laws of thermodynamics apply just fine to

finite system.

-- A Maxwell demon is a device that purports to violate the

2nd law of thermodynamics by looking for fluctuations. Such

devices never work as advertised, but they sometimes do other

interesting things; see Feynman, op.cit.

-- Other issues not yet identified.

-- Combinations of the above.

... applying macroscopic concepts like pressure, temperature and

volume to a system where they don't apply.

I'm not sure that's the whole story, or even the main part of the

story.

1) Actually the standard notions of pressure and volume apply just

fine to systems of all sizes (microscopic, moderately large, and

infinite). Temperature is not always well defined, but certainly

there are some systems, even microscopic systems, where it is well

defined.

2) Secondly, "macroscopic" is not quite the right word.

Any _finite_ system (whether macroscopic or microscopic) will exhibit

thermal fluctuations, and I think fluctuations are a big part of the

story here.

-- For microscopic systems, fluctuations dominate.

-- For medium-large systems, fluctuations lead to smallish

correction terms.

-- For infinite systems, fluctuations are negligible.

As far as I can tell, the issue here is not that the system is less

than macroscopic, but rather that it is less than infinite.

This is a pedagogical problem, because students typically start by

studying situations where fluctuations are negligible ... and they

may never get around to really understanding fluctuations.

This is quite a fundamental issue, affecting even our basic notion

of equilibrium. For finite systems, there will be fluctuations

/even at equilibrium/.

Also keep in mind that fluctuations are related to dissipation via

the _fluctuation / dissipation theorem_ ... which is a corollary

of the second law of thermodynamics. So understanding fluctuations

is part and parcel of any attempt to understand dissipation.

All this falls under the heading of "finite size effects". I just

now added a section on this to my thermodynamics document:

http://www.av8n.com/physics/thermo-laws.htm#sec-finite

As discussed there, finite size effects can be categorized as:

* Boundary effects;

* Quantization effects;

* Mean free path effects;

* Transport and dissipation effects; and

* Fluctuations.

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

Remark: This stuff is not trivial, and it is not old hat. Remember

that Einstein published the first real explanation of Brownian motion.

A hundred years ago, this was considered very advanced physics.

Even in 2009, you can still publish papers on Maxwell's demon.

http://arxiv.org/abs/0707.3400

Authors: Koji Maruyama, Franco Nori, Vlatko Vedral

Abstract:

Maxwell's demon was born in 1867 and still thrives in modern physics.

He plays important roles in clarifying the connections between two

theories: thermodynamics and information. Here, we present the

history of the demon and a variety of interesting consequences of the

second law of thermodynamics, mainly in quantum mechanics, but also

in the theory of gravity. We also highlight some of the recent work

that explores the role of information, illuminated by Maxwell's

demon, in the arena of quantum information theory.

**Follow-Ups**:**Re: [Phys-l] Temp & Energy density***From:*Jack Uretsky <jlu@hep.anl.gov>

**Re: [Phys-l] Temp & Energy density***From:*Brian Whatcott <betwys1@sbcglobal.net>

**References**:**Re: [Phys-l] Feynman's messenger lectures now available***From:*"Patricia T Viele" <ptv1@cornell.edu>

**Re: [Phys-l] Feynman's messenger lectures now available***From:*"Polvani, Donald G." <donald.polvani@ngc.com>

**[Phys-l] Temp & Energy density***From:*"Paul Lulai" <plulai@stanthony.k12.mn.us>

**Re: [Phys-l] Temp & Energy density***From:*Brian Whatcott <betwys1@sbcglobal.net>

**Re: [Phys-l] Temp & Energy density***From:*"Paul Lulai" <plulai@stanthony.k12.mn.us>

**Re: [Phys-l] Temp & Energy density***From:*John Mallinckrodt <ajm@csupomona.edu>

**Re: [Phys-l] Temp & Energy density***From:*"Paul Lulai" <plulai@stanthony.k12.mn.us>

**Re: [Phys-l] Temp & Energy density***From:*Donald Smith <dsmith4@guilford.edu>

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