# 19.30 Maxwell’s demon

Maxwell’s demon is an early example of a “thought experiment” (see post 19.26).

The Scottish physicist James Clerk Maxwell thought about two samples of a gas, each containing containing fast (red in the picture) and slow (blue) molecules, separated by a wall. He supposed that the wall contained a tiny door that could be opened or closed by a tiny demon. Remember, that in a gas, molecules in constant motion and are free to move throughout the space defined by the walls that contain them (post 16.37).

Now let’s suppose the demon opens the door whenever a slow molecule is moving towards left side and whenever a fast molecule is moving to the right; any other time he keeps it closed. Eventually the system will look like the picture below.

Remember that heat is kinetic energy of molecular motion (post 16.35) and that the greater the speed of the molecules, the higher their kinetic energy (post 16.21). So the right-hand side of the wall becomes hotter and the left becomes colder, as shown in the picture.

Heat appears to be flowing in a direction that makes something hotter and so appears to be contrary to the “second law of thermodynamics” (see post 16.34). You could also think of this process as the separation of fast and slow molecules – so decreasing the entropy of the system and breaking the seond law (post 16.38).  So, is Maxwell’s demon involved in breaking the second law of thermodynamics?

What do you think? When you’ve thought for a while, scroll down.

Keep thinking for a bit longer, before you scroll down!

The important thing about the second law is that it describes spontaneous flow of heat (post 16.34). The flow of heat described above is not spontaneous because of the intervention of the demon. A heat pump (a refrigerator) needs to do work (post 16.20) to makes the heat flow in the opposite direction to what would happen spontaneously (see post 18.30 for information about heat pumps). So, if the demon does work when opening and closing the door, he is simply behaving as the motor for a heat pump.

But I’ve cheated by not telling you everything about the demon. According to Maxwell, he could open and close the door without doing work. So, he does appear to be breaking the second law.

I’m not happy about this. If the demon (and his arms) have non-zero mass and the door has non-zero mass, he changes their momentum (post 16.13) whenever the door is moved to an “open” or “closed” position. This is another way of saying that he exerts a force (post 16.13). When he moves the door (and his arms) he moves the point at which the force acts, so he does work (post 16.20). The only way he can operate the door without doing work is if it (and he) have zero mass.

So, to believe in the whole story, we must believe that a moving object can be stopped by a door with no mass. I find this difficult to believe. So, let’s replace the physical door by some form of force field that the demon can turn on or off. But the action of switching the force field on and off still involves movement of the demon and some switching mechanism. This can only be achieved without doing work if the demon and the mechanism have no mass.

I think that Maxwell’s demon can only break the second law of thermodynamics, if it is possible to have an object with no mass (see post 16.13 to find out more about mass). I find it difficult to accept this idea for an object that must be bigger than a molecule.

The interesting thing about Maxwell’s demon is that different people interpret his thought experiment in different ways – as you will find if you search for it on the web. Many interpretations involve the idea of information. We can convey information by placing things in order. For example, we put letters in order to make words and words in order to makes sentences – this process enables us to convey information by writing. We can think of entropy as a lack of order (post 16.38), so that information is a process of decreasing entropy or increasing negative entropy, sometimes called negentropy. Now the second law is that negentropy cannot spontaneously increase. But the action of the demon caused an increase in negentropy, or information, (without doing work) because we now have an orderly pattern of blue and red molecules. These ideas form the basis of many opinions about Maxwell’s demon.

Finally, I believe that Maxwell’s demon is not breaking the second law. It doesn’t matter if we define the second law in terms of heat flow (post 16.34), increase in entropy (post 16.35), decrease in order (post 16.38) or decrease in information. It describes a spontaneous process. The intervention of the demon prevents any process from being spontaneous – so, I believe, the second law is not broken.

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