Physics, information, and computation

¶ … Demons

There are several theories in physics that apply probability theory to various problems. Examples of this can be statistical mechanics and statistical thermodynamics. Physicist James Clerk Maxwell came up with a thought experiment in the late nineteenth century that has puzzled people for over a century. The thought experiment deals with how someone might be able to violate the second law of thermodynamics by creating a situation that might decrease entropy in the system. Entropy can be thought of as the tendency for any system to loose energy. Entropy is a function of state, like the internal energy. It measures the relative degree of order (as opposed to disorder) of the system when in this state. An understanding of the meaning of entropy thus requires some appreciation of the way systems can be described microscopically (Sethna).

Maxwell had the insight to think of two systems placed side by side. He thought of two containers of gas side by side, both in equilibrium. The containers would be separated by an insulated door of some kind that could be opened and closed quickly. When the door was opened, it could be done so in a way that only allowed some of the molecules to enter the other side of the chamber. The molecules that were allowed to pass through the system would be the faster moving particles while the particles that remained would be the slower ones. This would result in the particles on one side of the chamber, the side that the faster particles would rest in, would gradually heat up while the other side cooled and decrease the total systems entropy.

The Experiment's Purpose

The experiment that Maxwell imagines deals with the average speed of molecules and how these are recorded as translating into heat and the temperature. However, if faster than average molecules are collected on one side of the container, then this would allow that side of the container to increase heat because it would have a greater proportion of the faster molecules. By contrast, the other side of the container would have the slower than average molecules and thus lose heat.

However the important part of the thought experiment is that both sides of the container would have slightly differing properties of temperature or pressure depending on the variances in the molecules speed. Thus, in one side of the container, there would be less entropy than otherwise because it is basically stealing the faster than average molecules from the other part of the container while replacing them with slower than average moving chemicals. Thus one side would not be subject to the normal entropy that would occur. As a result of the tank not undergoing entropy (at the same level) the assumption is made that the second law of thermodynamics can only be true based on statistical assumptions rather than in practice.

Figure 1 - Maxwell's Demon (Universe Review)

Discussion

In the work of Clausius, thermodynamics was considered to be completely universal and applicable without limit; just as Newton's law of gravitation applied to all matter in motion -- atoms, apples, and planets -- so too did thermodynamics apply to everything (Callender).The puzzle that Maxwell proposed help set up the framing of the conflicts between classical mechanics and thermodynamics. Many later physicists wondered in the second law of thermodynamics and even thermodynamics in general would apply to microscope systems. Maxwell himself believed that once humanity could witness the "micro-level" that these laws would break down. However, he didn't live long enough to see.

One of the problems with examining a system in the way that Maxwell's Demon experiment is designed is that it is difficult to know which level to frame the concept of thermodynamics at. For example, if the system is considered in isolation, and the terms of Maxwell's theory played out, then this could be evidence that the concept of entropy is statistical. However, on the other hand, the "demon" or the "valve" or whatever else is operating the insolated barrier between the containers would undoubtedly have to add some energy into the system to be able to perform that task. Thus such a criticism would add a level of perspective into the calculation and question whether or not someone could actually construct an isolated system such as Maxwell intended.

Other accounts have tried to explain how the entropy in the system is preserved by using molecules "information." This approach is similar to trying to look at a broader system but with information entropy rather than traditional entropy. If the "demon" only allowed some particles to pass and not others, then the demon must be able to store this information somehow. Then, since the demon would not be able to store information indefinitely because there is no infinite storage space for information, at some point some information must be discard. This would then create a form of information entropy that occurs in the system.

There have been many experiments that have been designed to study that have been based off of Maxwell's thought experiment. Many of the earlier attempts were able to show that the second law of thermodynamics was preserved by accounting for the "demon" in the experiment and the energy or information that this thing or individual added to the system. However the quest for Maxwell's puzzle has grown significantly more complex as time goes on. While some believe that they have shown proof that the system violates the second law, still others point to the role of the observer in the system. However, some have argued that (Callender):