Freethought & Rationalism Archive

Friar Bellows · 01-20-2003, 04:40 AM

As the great James Clerk Maxwell once wrote:

Quote:

The truth of the second law [of thermodynamics] is ... a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules ... Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules belonging to a real body.

About a decade ago this idea of small-scale violations of the second law of thermodynamics was given a more formal treatment, via the so-called Fluctuation Theorem (PDF link, 808 KB), which quantifies the probability of observing second law violations in small systems observed for a short time. Over the next few years, the theorem was refined and generalised by various scientists (including my former thesis advisor). Computer simulations had demonstrated the theorem in (virtual) action, but then last year real-world experimental confirmation was finally at hand. Here's a couple of links to the popular press reports:

Pushing the Second Law to the Limit

Law and Disorder: Chance fluctuations can rule the nanorealm

The significant thing about this experiment is that it demonstrates that what Maxwell calls a "sufficiently small group of molecules" may actually be quite larger than we might have thought, and this may have significant implications for scientists studying natural systems of that size (e.g. biochemists, biologists) or designing artificial systems of that size (e.g. nanotechnologists). An excerpt from one of the above news reports:

Quote:

The researchers used optical tweezers to grab hold of a micron-sized bead and drag it through water. By measuring the motion of the bead and calculating the minuscule forces on it, the researchers were able to show that the bead was sometimes kicked by the water molecules in such a way that energy was transferred from the water to the bead. In effect, heat energy was extracted from the reservoir and used to do work (helping to move the bead) in apparent violation of the second law.

As it turns out, when the bead was briefly moved over short distances, it was almost as likely to extract energy from the water as it was to add energy to the water. But when the bead was moved for more than about 2 seconds at a time, the second law took over again and no useful energy could be extracted from the motion of the water molecules, eliminating the possibility of micron-sized perpetual motion machines that run for more than a few seconds. Nevertheless, many physicists will be surprised to learn that the second law is not entirely valid for systems as large as the bead-and-water experiment, and for periods on the order of seconds. After all, even a cubic micron of water contains about thirty billion molecules. While it's still not possible to do useful work by turning water into ice, the experiment suggests that nanoscale machines may have to deal with phenomena that are more bizarre than most engineers realize.

OK, so Maxwell's Demon might not get his perpetual motion machine working, but maybe he'll dash our nanotechnology hopes!

Feather · 01-21-2003, 09:53 AM

Bah. Stat. Mech. will be rendered moot once we have computing machines that can efficiently manipulate calculations for 10^50 and more particles individually. Then we'd just need to know the relevent basic interactions (i.e. culoumb, gravitation, etc.) and the initial conditions. Plug into some numerical derivative/integral scheme and viola: completely determined system, as far as QM will allow.

Okay; okay so I dream and wish. So sue me.

fando · 01-21-2003, 10:31 AM

Hmm... seems like there won't be much hope for roaming nanobots. I can't picture how a nanomachine will traverse short distances in a fluid while keeping abreast of its orientation. I predict that the smallest functional multi-purpose robots will be cell sized, and even then they'll be of limited utility.

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01-21-2003, 09:53 AM	#2
Feather Veteran Member Join Date: May 2002 Location: Gainesville, FL Posts: 1,827	Bah. Stat. Mech. will be rendered moot once we have computing machines that can efficiently manipulate calculations for 10^50 and more particles individually. Then we'd just need to know the relevent basic interactions (i.e. culoumb, gravitation, etc.) and the initial conditions. Plug into some numerical derivative/integral scheme and viola: completely determined system, as far as QM will allow. Okay; okay so I dream and wish. So sue me.

01-21-2003, 10:31 AM	#3
fando Veteran Member Join Date: Sep 2001 Location: Los Angeles Area Posts: 1,372	Hmm... seems like there won't be much hope for roaming nanobots. I can't picture how a nanomachine will traverse short distances in a fluid while keeping abreast of its orientation. I predict that the smallest functional multi-purpose robots will be cell sized, and even then they'll be of limited utility.

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