The Information - James Gleick [131]
Eventually physicists began speaking of microstates and macrostates. A macrostate might be: all the gas in the top half of the box. The corresponding microstates would be all the possible arrangements of all particles—positions and velocities. Entropy thus became a physical equivalent of probability: the entropy of a given macrostate is the logarithm of the number of its possible microstates. The second law, then, is the tendency of the universe to flow from less likely (orderly) to more likely (disorderly) macrostates.
It was still puzzling, though, to hang so much of physics on a matter of mere probability. Can it be right to say that nothing in physics is stopping a gas from dividing itself into hot and cold—that it is only a matter of chance and statistics? Maxwell illustrated this conundrum with a thought experiment. Imagine, he suggested, “a finite being” who stands watch over a tiny hole in the diaphragm dividing the box of gas. This creature can see molecules coming, can tell whether they are fast or slow, and can choose whether or not to let them pass. Thus he could tilt the odds. By sorting fast from slow, he could make side A hotter and side B colder—“and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed.”♦ The being defies ordinary probabilities. The chances are, things get mixed together. To sort them out requires information.
Thomson loved this idea. He dubbed the notional creature a demon:
(Illustration credit 9.1)
“Maxwell’s intelligent demon,” “Maxwell’s sorting demon,” and soon just “Maxwell’s demon.” Thomson waxed eloquent about the little fellow: “He differs from real living animals only [only!] in extreme smallness and agility.”♦ Lecturing to an evening crowd at the Royal Institution of Great Britain, with the help of tubes of liquid dyed two different colors, Thomson demonstrated the apparently irreversible process of diffusion and declared that only the demon can counteract it:
He can cause one-half of a closed jar of air, or of a bar of iron, to become glowingly hot and the other ice cold; can direct the energy of the moving molecules of a basin of water to throw the water up to a height and leave it there proportionately cooled; can “sort” the molecules in a solution of salt or in a mixture of two gases, so as to reverse the natural process of diffusion, and produce concentration of the solution in one portion of the water, leaving pure water in the remainder of the space occupied; or, in the other case, separate the gases into different parts of the containing vessel.
The reporter for The Popular Science Monthly thought this was ridiculous. “All nature is supposed to be filled with infinite swarms of absurd little microscopic imps,” he sniffed. “When men like Maxwell, of Cambridge, and Thomson, of Glasgow, lend their sanction to such a crude hypothetical fancy as that of little devils knocking and kicking the atoms this way and that …, we may well ask, What next?”♦ He missed the point. Maxwell had not meant his demon to exist, except as a teaching device.
The demon sees what we cannot—because we are so gross and slow—namely, that the second law is statistical, not mechanical. At the level of molecules, it is violated all the time, here and there, purely by chance. The demon replaces chance with purpose. It uses information to reduce entropy. Maxwell never imagined