Maxwell's Demon

By Vijay Damodharan - Natural Sciences Student @ Christ College, Cambridge

 

The laws of thermodynamics are empirical laws that govern all processes in the universe.


Famously, the first and second laws are:

1. Total energy of an isolated system is conserved

2. Entropy of an isolated system cannot decrease


There are many ways of describing these laws, but they all mean the same thing.


Almost every known process obeys these norms, and they are used in solving many problems in science. So, when James Clerk Maxwell suggested a thought experiment in 1867 which supposedly violated the second law, it was the topic of much discussion.


Let’s begin by defining the key terms. An ‘isolated system’ is a system such that energy and particles cannot flow into or out of the system. In simple terms, entropy is a measure of the amount of disorder in a system.


In other words, the second law says that systems will always get more disordered by nature unless you put in the energy to keep them ordered. For example, your room will become messy over time, unless you put in the effort to maintain it. Another consequence of the second law is that if you put two objects of unequal temperatures in thermal contact, they will reach the same temperature after some time. This second idea will become important in our following discussion.


What Maxwell proposed is the following. Imagine a box filled with particles at some temperature. The particles will be moving at various speeds, in various directions, and occupying the entire box. Now suppose the box had a wall or a partition in the middle, equipped with a small door.


This door is controlled by a demon who has senses sharp enough to detect every particle that comes close to the door. The demon decides that if a particle travelling to the left has a higher-than-average velocity, he will open the door and let it move to the left side of the box. Similarly, if a particle moving to the right has a lower-than-average velocity, he will open the door and let it move to the right side of the box.


If we wait long enough, we will end up in a situation where the left-hand side has particles which are all moving much faster on average than particles on the right-hand side of the box. Since temperature is a measure of the average kinetic energy of the particles, we have made a box, that was originally at a uniform temperature, separate into a part that is hot on the left and cold on the right, (seemingly) without putting any energy in!


If such an experiment could be designed (using a detector to replace the demon of course) then it seems that it would violate the second law of thermodynamics.


After this thought experiment was suggested, many possible solutions were put forth. The first revolved around the detection process. To detect a particle, you need to use photons (particles of light). If there were no particles present, the photon would reach a detector, but if there were, then the photon would disperse the particle and they would not reach the detector. The scattering of particles would increase entropy, and, after some calculations, people showed that this increase would be greater than the decrease in entropy caused by separating the temperatures.


However, this argument became redundant when a method of measurement which appeared to be reversible was proposed which would therefore not cause an increase in entropy.


Later, it was argued that in detecting and measuring the velocities of the particles, you would need to collect, store, and delete information. The latter would increase entropy, which would negate the decrease in entropy due to separating the temperatures.


Another key thing to consider is the mechanism of the trap door itself. For a trap door to work, we need the door to be able to close and remain shut, or open and remain open. However, on its own, an object would just do the Brownian motion (vibrate randomly). So, to make a door exist in a state of only open or close, we need to build an energy barrier that separates the two states, so that the door cannot just randomly open and close due to its natural vibrations.


However, to open or close that door, you must provide enough energy to overcome that energy barrier so that it may change state. This energy cannot be recovered and would be dissipated as heat in the surroundings, which would cause an increase in entropy as well.


The Maxwell Demon problem shows a good example of a setup, which, at first glance, appears to violate a fundamental law of physics, but upon careful consideration of the various components involved this proves to be false.


There is an important lesson to be learnt from this problem as well. Any process which achieves a determined result, such as moving the trap door or measuring a particle, must be an irreversible process.


In other words, all measurements are irreversible processes. The measurement process in quantum mechanics is one of the biggest mysteries in physics, but perhaps thinking about it in terms of entropy and irreversible processes could shed some light on what is going on.


Further Reading:


1. Wikipedia Contributors (2021). Maxwell’s demon. [online] Wikipedia. Available at: https://en.wikipedia.org/wiki/Maxwell%27s_demon

2. O’Callaghan, J. (2021). How Maxwell’s Demon Continues to Startle Scientists. [online] Quanta Magazine. Available at: https://www.quantamagazine.org/how-maxwells-demon-continues-to-startle-scientists-20210422/

3. Mizraji, E. (2021). The biological Maxwell’s demons: exploring ideas about the information processing in biological systems. Theory in Biosciences. doi:10.1007/s12064-021-00354-6 (explores biological Maxwell’s demon and is slightly more complex than the other two sources)