Using Information to Extract Energy

There was some excitement last week about a Maxwell's-Demon-type experiment conducted by Shoichi Toyabe and collaborators in Japan. (Costly Nature Physics article here; free arxiv version here.) It's a great result, worth making a fuss about. But some commentators spun it as "converting information into energy." That's not quite right -- it's more like "using information to extract energy from a heat bath." Say you have a box of gas with a certain temperature at maximum entropy -- thermodynamic equilibrium. That is, the gas is smoothly spread throughout the box. (We can safely ignore gravity.) There's certainly energy in there, but it's not very useful. Indeed, one way of thinking about entropy is as a measure of how useless a certain amount of energy is. If we have a low-entropy configuration, we can extract useful work from the energy inside, such as pushing a piston. If we have a high-entropy configuration, the energy is useless; there's nothing we can do to consistently extract it. Here's an example from my book. Consider two pistons with the same number of gas particles inside, with the same total energy. But the top container is in a low-entropy state with all the gas on one side of the piston; the bottom container is in a high-entropy state with the gas equally spread out.