Complexity_ A Guided Tour - Melanie Mitchell [22]
FIGURE 3.1. Top: James Clerk Maxwell, 1831–1879 (AIP Emilio Segre Visual Archives) Bottom: Maxwell’s Demon, who opens the door for fast (white) particles moving to the left and for slow (black) particles moving to the right.
According to the second law, work has to be done to decrease entropy. What work has been done by the demon? To be sure, he has opened and closed the door many times. However, Maxwell assumed that a massless and frictionless “slide” could be used as a door by the demon, so that opening and closing it would require negligible work, which we can ignore. (Feasible designs for such a door have been proposed.) Has any other work been done by the demon?
Maxwell’s answer was no: “the hot system [the left side] has gotten hotter and the cold [right side] colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed.”
How did entropy decrease with little or no work being done? Doesn’t this directly violate the second law of thermodynamics? Maxwell’s demon puzzled many of the great minds of the late nineteenth and early twentieth centuries. Maxwell’s own answer to his puzzle was that the second law (the increase of entropy over time) is not really a law at all, but rather a statistical effect that holds for large collections of molecules, like the objects we encounter in day-to-day life, but does not necessarily hold at the scale of individual molecules.
However, many physicists of his day and long after vehemently disagreed. They believed that the second law has to remain inviolate; instead there must be something fishy about the demon. For entropy to decrease, work must actually have been done in some subtle, nonapparent way.
Many people tried to resolve the paradox, but no one was able to offer a satisfactory solution for nearly sixty years. In 1929, a breakthrough came: the great Hungarian physicist Leo Szilard (pronounced “ziLARD”) proposed that it is the “intelligence” of the demon, or more precisely, the act of obtaining information through measurement, that constitutes the missing work.
Szilard was the first to make a link between entropy and information, a link that later became the foundation of information theory and a key idea in complex systems. In a famous paper entitled “On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings,” Szilard argued that the measurement process, in which the demon acquires a single “bit” of information (i.e., the information as to whether an approaching molecule is a slow one or a fast one) requires energy and must produce at least as much entropy as is decreased by the sorting of that molecule into the left or right side of the box. Thus the entire system, comprising the box, the molecules, and the demon, obeys the second law of thermodynamics.
In coming up with his solution, Szilard was perhaps the first to define the notion of a bit of information—the information obtained from the answer to a yes/no (or, in the demon’s case, “fast/slow”) question.
Leo Szilard, 1898–1964 (AIP Emilio Segre Visual Archives)
From our twenty-first-century vantage, it may seem obvious (or at least unsurprising) that the acquisition of information requires expenditure of work. But at the time of Maxwell, and even sixty years later when Szilard wrote his famous paper, there was still a strong tendency in people’s minds to view physical and mental processes as completely separate. This highly ingrained intuition may be why Maxwell, as astute as he was, did not see the “intelligence” or “observing powers” of