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Sunday 28 October 2012

Maxwell’s Demon

There was a two-part documentary on BBC4 last week called Order and Disorder, which among other things discussed the subject of Maxwell’s Demon (left, with presenter Jim Al-Khalili). Maxwell’s Demon is the only demon you are likely to come across in the average physics textbook, and—as far as I know—the only supernatural entity that has been subjected to rigorous scientific analysis. But it turns out the analysis has major implications for any purported “supernatural being” of a non-physical nature, whether you call it a demon, angel, ghost or anything else.

The aim here isn’t to prove or disprove the existence of non-physical entities, but to address the question of whether—if such entities exist—they would be able to interact with the physical world in a way that breaks the laws of physics. At first sight, this is a no-brainer: surely a non-physical entity, by definition, can act outside the constraints of physical laws. But the catch is in the word “interact”—it turns out that as soon as the demon (or whatever) tries to interact with the physical world, it finds itself caught up in the inexorable laws of physics.

Many physics students will have encountered Maxwell’s Demon in their first year at university. This particular demon is the central character in a “thought experiment” originally proposed by James Clerk Maxwell in 1871. The experiment involves a box divided by an impermeable partition into two halves, each containing air that is initially at the same temperature. In other words, the two halves of the box start out in thermal equilibrium. The demon is imagined to be microscopically small, with hyper-acute senses that can detect the motions of air molecules on both sides of the partition. By some unspecified supernatural (non-physical) means the demon is assumed to operate a tiny shutter in the partition—allowing slower-moving molecules to move from the left-hand side to the right-hand side, and faster moving molecules from the right-hand side to the left-hand side. Over time the left-hand side will become hotter and the right-hand side cooler—in other words, the two halves are no longer in thermal equilibrium.

This situation is a direct violation of the Second Law of Thermodynamics—or to put it in layman’s terms, it breaks one of the fundamental laws of physics. The fact that Maxwell’s Demon is a demon—a non-physical, supernatural entity—is absolutely crucial to the thought experiment. It’s not that Maxwell, with the limitations of his Victorian perspective, had never heard the word “nanobot” so he used the word demon instead. A nanobot, if such a thing existed, couldn’t do what the demon can do. A nanobot, being a part of the physical world, wouldn’t violate the Second Law of Thermodynamics. It would have to expend energy in opening and closing the shutter, and that’s fine—moving heat from one place to another by expending energy is what Victorian thermodynamics was all about. The thought experiment only works if the demon is a truly non-physical entity.

Personally I suspect Maxwell would have been astonished that his thought-experiment would feature so prominently in a TV documentary about information theory almost a century and a half later. I don’t think he had any such profound implications in mind. I think he was just trying to dramatize the point that the Second Law of Thermodynamics is predicated on an assumption of randomness, and that if something intervened to compromise that randomness then the Law would no longer be true. This contrasts with other scientific laws of the time, such as the Law of Gravity or Maxwell’s equations of electromagnetism, which don’t require any assumptions of randomness.

In the TV programme, however, Jim Al-Khalili presented the story of Maxwell’s Demon as if Maxwell had some visionary inkling of 21st century information theory and was struggling to get to grips with it. While I’m sure that’s romantic nonsense, the fact remains that 21st century information theory does have something startling to say about Maxwell’s Demon. It turns out that, if the essential information processing that has to go on inside the Demon’s brain is taken into account, then it doesn’t violate the Second Law of Thermodynamics after all.

As I said at the beginning, I suspect this is a general result for all supernatural entities, real or imagined, that try to interact with the physical world. No matter how non-physical they are themselves, at some level they have to conform to the laws of the physical universe when they interact with it.


Ross said...

A "supernatural," non-physical entity (a demon, in this case) wouldn't have a brain, which is a natural, physical organ.

Andrew May said...

No, that's perfectly right. It was sloppy of me to say "inside the demon's brain", although a similar phrase was used in the TV programme. The point they were making though is that information has to be processed somehow, and this has to obey the Landauer limit.

Ross said...

It's curious to me that it is so often assumed that entities such as ghosts, demons, etc., are supernatural or non-physical. After all, they impinge on our physical senses, and they seem to make use of physical factors (such as energy). Even if they are non-material, that doesn't necessarily mean they are non-physical. Maybe it would make more sense to view them as natural, physical entities until proven otherwise. (Of course, I am aware that some people regard the very existence of such entities as unproven.)

Andrew May said...

I agree completely. If such entities exist, they are most likely an aspect of the physical world that is not yet understood -- and hence obey physical laws even if the laws in question are ones we don't properly understand. However, I had always had in the back of my mind that they might be non-physical, I.e. pure information content that is encoded in some non-physical way. I'm particularly thinking of ghosts here. But if I understood the Landauer argument correctly, there is no such thing as information that is totally separable from physical concepts such as energy. But I'm out of my depth here!