James Clerk Maxwell is best known for predicting the speed of light from equations that bear his name. As a mathematical theorist, he was also interested in statistical mechanics—the theory that explains the behavior of gasses in terms of the motions of molecules (in contrast to thermodynamics, which describes visible behavior in terms of heat flow, volume, pressure, and temperature). The Second Law of Thermodynamics was a hot topic in the 19th century, since it seemed to imply that the universe is dissipating toward an ultimate “heat death.” It says, basically, that the overall amount of order in the universe cannot increase, that the efforts we make to extract useful energy and create local order always result in more overall disorder or useless energy. There are no perpetual motion machines and no free lunches. This has implications for the limits of efficient computation.
Long before computers, Maxwell was suspicious of efforts to prove the 2nd Law using statistical mechanics. He devised a thought experiment to express his concerns. Imagine a container of gas with a central partition. A hole in this partition allows molecules to pass from one chamber to the other, so that pressure and temperature would equalize over time. But imagine also a clever little fellow inside who “effortlessly” operates a frictionless hatch, placed over the hole, in such a way as to admit only fast-moving molecules, one way into one chamber. With no work invested, this would eventually create a higher temperature or pressure on one side than on the other. Work could be extracted from this difference in a repeatable cycle (e.g., by moving a piston)—apparently contradicting the 2nd Law. Physicists have long debated the implications of this seeming paradox, trying to exorcise Maxwell’s demon or prove whether the 2nd Law is inviolable. It’s still unclear whether it should be thought of as a precise matter of principle or as only true on average, and how it might apply to the cosmos as a whole.
Thought experiments are always idealizations, contrived to explore a crucial issue in situations where many variables would actually be in play. Maxwell’s “demon” is a disembodied intelligence whose physical properties are disregarded. The demon and the hatch are massless and require no energy to move. The demon defies a law of physics by evading physics in the first place. The challenge of the thought experiment is to understand the exact nature of the crime.
Life is a process that creates local order using energy. If the 2nd Law is unconditionally true, then just by existing we contribute to the overall increase of entropy. On the other hand, since the universe is still in a relatively ordered state, it must have begun in an even more ordered state, for the 2nd Law implies a running down with time. Where did that initial order come from? The ultimate demon, God? Or, is it possible that order arises naturally, without or despite a growing total of disorder?
Actual experiments too are idealizations. So are laws of physics, which not only summarize experimental results, but are often supposed to cause those results. Maxwell’s Demon points to general questions about the role of theory, idealization and physical law. Do natural laws pre-exist the universe, guiding its formation, or do they simply tally what we see? Do they even describe reality, or merely human conceptual systems? Such questions reflect the awkwardness with which we embrace our ambivalent status as both physical and mental beings. Like Maxwell’s Demon, we are ambiguously participants and observers, standing at once inside and outside the system of the world—hoping always for a free lunch.