Maxwell's Demon
A tiny demon sits at a trapdoor between two chambers of gas, letting fast molecules through one way and slow ones the other. The demon sorts hot from cold without doing work, apparently violating the second law of thermodynamics. What's wrong with this picture?
James Clerk Maxwell proposed this demon in 1867 to probe the statistical foundations of thermodynamics. The puzzle remained open for decades. The resolution, developed by Rolf Landauer in 1961 and Charles Bennett in 1982, connected information theory and physics in a surprising way: erasing information costs energy.
Maxwell, J.C. (1867). Letter to Peter Guthrie Tait. In P.M. Harman (Ed.), The Scientific Letters and Papers of James Clerk Maxwell.
The setup
Two chambers of gas are separated by a wall with a tiny trapdoor. A demon controls the door. When a fast-moving molecule approaches from the right, the demon opens the trapdoor and lets it through to the left. When a slow-moving molecule approaches from the left, the demon lets it through to the right.
Over time, fast molecules accumulate on the left and slow ones on the right. Temperature difference emerges from equilibrium. The demon has created usable energy without doing any work, apparently beating entropy.
But the second law of thermodynamics says entropy always increases in a closed system. Something has to give.
The resolution: it's about memory
For nearly a century, physicists tried to find the flaw. The breakthrough came when people noticed that the demon has to remember which molecules are fast and which are slow in order to sort them.
Landauer showed that erasing information has a minimum energy cost. The demon's act of forgetting, clearing its notes at the end of each cycle, necessarily generates exactly the entropy the sorting removed. The second law holds.
The remarkable conclusion: information is physical. The act of erasing a bit of information generates at least kT·ln2 of heat, where k is Boltzmann's constant and T is temperature.
Why it matters beyond physics
The Maxwell's Demon puzzle connected three things that seemed separate: thermodynamics, information theory, and computation. Every time a computer erases data, it necessarily generates heat. There is a fundamental physical limit to how efficiently you can compute.
And more broadly: it showed that information isn't an abstract thing floating above reality. It has physical consequences.