Information Theory - Part 2: Maxwell's Demon

How can a theory about information and noise be considered as profound as relativity and quantum theory? Sounds ridiculous, right? So let’s check out the first big science-y problem that information theory solved.

The second law of thermodynamics forbids the existence of a perpetual motion engine (That’s a machine that can run forever without any intervention that involves more work than the work you get from the machine itself). Why not, asked James Clark Maxwell, with his famous thought experiment known as Maxwell’s demon, devised in 1871.

But first, a recap of some basics. Heat flows from a hotter to a colder place. As that heat flows, you can use (part of) that heat flow to do work. By definition, this means that once the two sides are at the same temperature (same heat), heat stops flowing (neither end is hotter anymore). And without heat flow, no work can be done.

We also know that heat is just a measure of the average speed of molecules. And since those molecules have random speeds, some would be faster than others. Enter Maxwell’s demon:

1)      Take a container with a gas inside it and a barrier at the center. Some molecules would be moving faster (red), others slower (blue).

2)     The demon would measure the speed of a molecule approaching the barrier and open/close the barrier to ensure the faster molecules end up on one side and the slower ones on the other side. Pics from this site.

3)      Eventually, all the faster molecules will be on one side and the slower ones on the other side.

4)      By definition, the side with the faster molecules has a higher temperature than the other side with the slower molecules.

5)     Now connect the two side (without the demon) and heat will flow from the hotter to the colder side.

6)     Tap into that flowing heat to get some work done.

7)     Once the two sides get to the same temperature, heat would stop flowing. Bring in the demon again and repeat steps 2 to 7. Endlessly. And voila! You have a system that can work endlessly. The demon was just utilizing the inherent speeds of the molecules, not speeding or slowing them down!

Nobody could explain the flaw in this thought experiment. Until, in 1982, information theory solved the puzzle. The key lay in the realization that the demon is an information processing machine (measure speed; close/open the partition based on measured value). Information processing involves writing, reading and erasing information. No matter how large the memory of the demon, at some point he runs out of it, and then he has to erase to “make space” to continue doing what he does. It is that last action (erasing) that increases the entropy of the system (box + demon) more than the reduction of the entropy of the container. As Charles Seife put it in Decoding the Universe:

“Bennett proved that the demon always has to reduce entropy of the container at a cost: a cost of memory, and then at a cost of entropy of the universe. There was no free ride, no perpetual motion machine. Maxwell’s demon was dead at the age of 111.”

Information theory had solved one of the longest standing problems in physics!