doom@portia.stanford.edu (Joseph Brenner) (03/04/90)
[Looks like the line-eater is back, or something. This msg
arrived starting in mid-sentence. --JoSH
thermodynamic cylinder with gas in it. The H =========== H
gas molecules bang around randomly inside the H<> /^ /\ ^_/\H
cylinder, exerting some pressure on the plunger H >< / x_/ ><H
(so that, for example, the plunger will slide H< | X \L/ /H
upwards if you increase the temperature) [see H \/ \/\ / \/ H
fig 1 -- and your imagination -- to the right]. H_V\ /__v__/\_H
---------------
{T}
...From a statistical mechanics point of view, H | H
there's a hypothetical condition where *all* of H =========== H
the gas molecules could just happen to travel H ^ ^ ^^ ^ H
in a parallel direction against the plunger. H | | || | H
Ideally, they could be repeatedly reflected H | | || | H
back and forth. But if that happened, the H | | || | H
pressure on the plunger would oscillate... H_V__V__VV__V_H
And then you could put a transducer on the end
(a piezo?) to convert some of this motion into a useful form of
energy, like an AC current, and in the process "cool" the gas.
Which means you've got something like a device that totally converts
heat into energy, which is supposed to be impossible. I think that
the orthodox objection is that this just shows that the laws of
thermo are probabilistic: the hypothetical condition above is wildly
improbable, hence in all real world cases this
will never happen.
{T}
But... what if you make the cylinder really H | H
small? What if it had only one molecule bouncing H =========== H
around in it? And what if you could construct H /\ /> H
billions of them, all ganged together? H< \ // H
H \ \ / H
The you get a nano-mechanical perpetual motion H \ / H
machine of the second type... H______\/_____H
So, what am I doing wrong? Is there a cold sink I'm missing somewhere?
(J.JBRENNER@MACBETH.STANFORD.EDU Materials Science Dept/Stanford, CA 94305)
[Ok. As well as I'm able to tell, the problem comes in when you
assume that you will be able to convert a periodic motion of the
piston at the molecular level to useful work. Remember that,
assuming that everything is at the same temperature, each molecule
in the whole structure is undergoing vibration, presumeably with
lots of nice periodic modes, with the same kinetic energy as the
molecule in the cylinder.
When you assume that you can build any mechanism that can be built
at a macroscopic scale, such as a ratchet crank, to take useful
energy off the piston's motion, you tend to think in terms of
solid, continuous objects, which can be made to stand still at
the appropriate times. Now the hidden source of energy becomes
more obvious: such parts would be an absolute zero heat sink.
In reality, such parts don't exist. You must try to design the
ratchet crank from parts made of balls strung together with springs--
and each ball is vibrating with the same kinetic energy as the
molecule in the cylinder. Now only a fraction of that energy
would be imparted to the piston each collision-- so each molecule
of each component of the mechanism is vibrating with much more
energy as that you're trying to capture from the piston's motion.
The same sort of thing happens when you try to design a spring trap
door or the like to be a nano-mechanical Maxwell's Demon.
--JoSH]hcobb@walt.cc.utexas.edu (Henry J. Cobb) (03/06/90)
This was covered in an article in Sci American. (Gee I'm making a habit of quoting SA to deflate the highly inflated schemes posted to this newsgroup ;-). The problem is that the control device must expend as much energy to forget the state of the device as it could posibly recive from the impact of the 'gas' molecule. The moral (for RAM designers ;-) is: 'Tis easy to remember, but forgetting takes effort'. Henry J. Cobb hcobb@ccwf.cc.utexas.edu "And may all your nanobots die of frozen rot." --- Me. [Boy, that's putting it concisely. Let me try to elaborate: The first thing that needs saying here is that we are really talking about entropy and not energy. Entropy is information; the entropy of a system in any given macrostate (ie, knowing things like volume, temperature, pressure) can be thought of as the number of bits necessary to tell which microstate (ie, tell me the position and velocity of each atom) that macrostate could represent. Now, we all know that at the macro level, useful work can be obtained in a closed system at the expense of raising its entropy--if we have two containers, one with a hot fluid in it, the other cold, we can run a heat engine off the "flow of heat" until they equalize (which macrostate has a higher entropy than the initial one). All of the Maxwell's demon schemes basically come down to an attempt to build a device that "eats" entropy, so that one can balance it with an entropy-raising device and produce endless work. (Usually such schemes actually obey energy conservation; that is why they're so seemingly paradoxical!) The great problem is that the laws of physics are reversible at the micro level. That means that I cannot have a system which starts in either micro-state A or B and ends up in microstate C either way; running it back from C I'd get (say) A only, and the process B-C wouldn't be reversible. Thus I can't build a machine that *truly* destroys a bit of information. I could always in theory, run it backward, and recover the bit. So if if I have a machine which appears to destroy a bit (such as a Maxwell's demon which cuts the possible positions of an atom in half) the resulting MACROstate must have a "hidden" bit of entropy separating those microstates that came from destroying a 1 and those from destroying a 0. So entropy has increased after all. (All this having been said, I should point out that there really exist entropy-eating objects: black holes. You can build machines that are impossible under the second law if they include a black hole--although a purist might debate whether they were "closed systems"!) --JoSH]
doom@portia.stanford.edu (Joseph Brenner) (03/07/90)
--------- About JoSH's objection: Certainly the "rubbery" nature of the cylinder I was proposing causes problems, but how would you prove that they make the device impossible? I might try and argue that the kinetic energy is not be equal, just the thermal energy, and that the somewhat greater stiffness of the cylinder might let you see the motion of the gas molecule as a very small "signal" on top of the thermal "noise" of the cylinder. Another way to look: can you build a piezoelectric crystal so small that it's thermal fluctuations can be detected as a voltage across the crystal? I would guess that if you could, you'd have a 2nd law violation, hence I expect you can't, but why not? In general about these comments: It seems to me that the nature of this game is that you can't just say "this contradicts the second law, therfore it's impossible". The idea is to find an inherent design flaw working from the ground up, and hence verify the second law. I would be suprized (to say the least) if I get anything out of this than a somewhat improved understanding of thermo... So, I'll re-read Drexler on the Maxwell's nano-Demon disproof, and I'll even try flipping though some recent SA's to see if I can trace Henry Cobb's reference. Thanks for the comments. -- Joe B. [I don't know that anything about nano-Demons is in EoC--I couldn't find anything in a quick review. Look at Cellular Automata Machines by Toffoli and Margolus (and papers by either, and by Fredkin) and the oft-mentioned Emperor's New Mind by Penrose for a nice overview of entropy matters (skip the AI part). I would imagine you get some voltage variation in any material directly due to the electronic component of the thermal energy, it doesn't have to be piezo-electric. The same arguments would apply to it as to mechanical motion--you'll have as hard a time building a diode for nano-voltages as a ratchet for nano-motions. There is no proof in my original reply--it was just explanatory. The proof, if you need one, would have to be built up from the reversibility of physics at the micro-level. --JoSH]