Everyday Entropy: Maxwell’s demon


You’ll never see a true image of particles in motion

Maxwell’s demon is a thought.  It was conceived in the decade after Clausius established entropy’s relationship to the transfer of energy and the second law of thermodynamics in the mid-nineteenth century.  As Maxwell put it,

“… if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.”

The relationship between information and energy was unknown at the time.  As an idea, the demon may have no mass or energy requirements, but in the real world information cannot move without energy; information cannot be forgotten without the application of energy to erase it; and finally, the “sharpened” facilities Maxwell envisioned cannot exist.  Light does not resolve the location of particles on the scale of gas molecules, which are a thousand times smaller than the wavelength of visible light, and any other means of obtaining information from the particles would throw them randomly off course, which would render useless whatever information was obtained.  Any particle on the scale of Brownian motion is too small to transmit information independent of its momentum, and in this way, at that scale, energy and information are unified and indistinguishable.
At larger scales, information, energy and mass go their separate ways.  The information about a bowling ball is distinguishable from its energy and its mass.  The thought of Maxwell’s demon is not the same as the energy used to process the idea and render it for the mind, and both are distinguishable from the mass of the mind considering the thought.  But down at the scale where Maxwell’s demon would have to do his dirty work, mass, energy and information are not distinguishable in meaningful terms; not for physicists; not for philosophers; not even for the thought that is Maxwell’s demon.
When someone says that information will make your process more efficient, be sure to ask how they plan to gather the information, and how they plan to get rid of it. The cost of junk data is not nothing.

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