How Maxwell’s Demon Continues to Startle Scientists



The universe bets on disorder. Imagine, for example, dropping a thimbleful of red dye into a swimming pool. All of those dye molecules are going to slowly spread throughout the water. Physicists quantify this tendency to spread by counting the number of possible ways the dye molecules can be arranged. There’s one possible state where the molecules are crowded into the thimble. There’s another where, say, the molecules settle in a tidy clump at the pool’s bottom. But there are uncountable billions of permutations where the molecules spread out in different ways throughout the water. If the universe chooses from all the possible states at random, you can bet that it’s going to end up with one of the vast set of disordered possibilities.

Seen in this way, the inexorable rise in entropy, or disorder, as quantified by the second law of thermodynamics, takes on an almost mathematical certainty. So of course physicists are constantly trying to break it.

One almost did. A thought experiment devised by the Scottish physicist James Clerk Maxwell in 1867 stumped scientists for 115 years. And even after a solution was found, physicists have continued to use “Maxwell’s demon” to push the laws of the universe to their limits.

In the thought experiment, Maxwell imagined splitting a room full of gas into two compartments by erecting a wall with a small door. Like all gases, this one is made of individual particles. The average speed of the particles corresponds to the temperature of the gas — faster is hotter. But at any given time, some particles will be moving more slowly than others.

What if, suggested Maxwell, a tiny imaginary creature — a demon, as it was later called — sat at the door. Every time it saw a fast-moving particle approaching from the left-hand side, it opened the door and let it into the right-hand compartment. And every time a slow-moving particle approached from the right, the demon let it into the left-hand compartment.

After a while, the left-hand compartment would be full of slow, cold particles, and the right-hand compartment would grow hot. This isolated system would seem to grow more orderly, not less, because two distinguishable compartments have more order than two identical compartments. Maxwell had created a system that appeared to defy the rise of entropy, and thus the laws of the universe.

“He tried to prove a system where the entropy would decrease,” said Laia Delgado Callico, a physicist at King’s College London. “It’s a paradox.”

Two advances would be crucial to solving Maxwell’s demon. The first was by the American mathematician Claude Shannon, regarded as the founder of information theory. In 1948, Shannon showed that the information content of a message could be quantified with what he called the information entropy. “In the 19th century, no one knew about information,” said Takahiro Sagawa, a physicist at the University of Tokyo. “The modern understanding of Maxwell’s demon was established by Shannon’s work.”

The second vital piece of the puzzle was the principle of erasure. In 1961, the German American physicist Rolf Landauer showed that any logically irreversible computation, such as the erasing of information from a memory, would result in a minimal nonzero amount of work converted into heat dumped into the environment, and a corresponding rise in entropy. Landauer’s erasure principle provided a tantalizing link between information and thermodynamics. “Information is physical,” he later proclaimed.

In 1982, the American physicist Charles Bennett put the pieces of the puzzle together. He realized that Maxwell’s demon was at core an information-processing machine: It needed to record and store information about individual particles in order to decide when to open and close the door. Periodically it would need to erase this information. According to Landauer’s erasure principle, the rise in entropy from the erasure would more than compensate for the decrease in entropy caused by the sorting of the particles. “You need to pay,” said Gonzalo Manzano, a physicist at the Institute for Quantum Optics and Quantum Information in Vienna. The demon’s need to make room for more information inexorably led to a net increase in disorder.

Acknowledgement and thanks to:: Quanta | Jonathan O'Callaghan
June 12, 2022