Random thoughts on Maxwell's demon

  • Thread starter ThomasT
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That's a... ...party trick.
This is what I'm trying to emphasize! The result achieved by extraordinary means is no more important than a party trick unless the result, itself, is extraordinary, in and of itself.

Suppose a magician actually used real magic to create a rabbit from nothing and pull it out of a hat. It would be conceptually astounding, he'd have broken all the laws of physics and completely upset the known paradigm. And all he'd have accomplished, though, is to create a new rabbit! We already have plenty of rabbits. A new rabbit is a trivial change to humanity. Rabbits already breed...like rabbits.

Why is the means whereby it's accomplished so important when the result is so mundane? I guess it depends on whether you're ultimately into concepts or practical realities.

The significance of the story, which is what ThomasT asked about, lies down a completely different path, one which just about everyone seems to miss: as I mentioned earlier, Maxwell wasn't proposing we should apply ourselves to figuring out how to get round the 2nd law, nor was he making a point about how the 2nd law was inviolate. He was making some completely different point about scale and statistical analysis:

Maxwell said:
This is only one of the instances in which conclusions which we have drawn from our experience of bodies consisting of an immense number of molecules may be found not to be applicable to the more delicate observations and experiments which we may suppose made by one who can perceive and handle the individual molecules which we deal with only in large masses.
His exact point seems to be nothing more than to say that we have to give careful consideration to what conclusions we are drawing about the microscopic situation from macroscopic analyses, the specific illustrative example being that the temperature we ascribe to some container of gas actually says nothing about the energy of any actual given molecule of gas we might observe if we could observe an individual molecule, that if you could actually separate the more energetic ones from the less energetic, both portions would deviate a lot, one being higher, the other lower, from the measured temperature of the gas.

On the other hand, his concluding paragraph asserts that sometimes a macroscopic statistical average actually reflects a microscopic uniformity, the example given being the mass of a hydrogen molecule:

Maxwell said:
I do not think, however, that the perfect identity which we observe between different portions of the same kind of matter can be explained on the statistical principle of the stability of the averages of large numbers of quantities each of which may differ from the mean. For if of the molecules of some substance such as hydrogen, some were of slightly greater mass than others, we have the means of producing a separation between molecules of different masses, and in this way we should be able to produce two kinds of hydrogen, one of which would be somewhat denser than the other. As this cannot be done, we must admit that the equality which we assert to exist between the molecules of hydrogen applies to each individual molecule, and not merely to the average of groups of millions of molecules.
His original goal was:

Before I conclude, I wish to direct attention to an aspect of the molecular theory which deserves consideration.
And that "aspect" of molecular theory he's directing our attention to, seems to be that, sometimes you are averaging a huge number of different things, at others you are averaging a huge number of uniform things. Careful consideration should be given to which is which least the microscopic reality be misunderstood.

The interjected question:

Maxwell said:
It would be interesting to enquire how far those ideas about the nature and methods of science which have been derived from examples of scientific investigation in which the dynamical method is followed are applicable to our actual knowledge of concrete things, which, as we have seen, is of an essentially statistical nature, because no one has yet discovered any practical method of tracing the path of a molecule, or of identifying it at different times.
Asks to what extent knowledge applies from one scale to the other. (In a sense, he's prematurely anticipating quantum physics.)
 

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