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How Maxwell’s Demon Continues to Startle Scientists

By Jonathan O'Callaghan

April 22, 2021

The thorny thought experiment has been turned into a real experiment — one that physicists use to probe the physics ofinformation.

It took physicists 115 years to tame Maxwell’s Demon.

Samuel Velasco/Quanta Magazine

The universe bets on disorder. Imagine, for example, dropping a thimbleful of red dye into a swimming pool. All of those dyemolecules are going to slowly spread throughout the water. Physicists quantify this tendency to spread by counting the number ofpossible 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 ofpermutations where the molecules spread out in different ways throughout the water. If the universe chooses from all the possiblestates 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 analmost mathematical certainty. So of course physicists are constantly trying to break it.

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

In the thought experiment, Maxwell imagined splitting a room full of gas into two compartments by erecting a wall with a smalldoor. Like all gases, this one is made of individual particles. The average speed of the particles corresponds to the temperature ofthe 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 everytime 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 thantwo identical compartments. Maxwell had created a system that appeared to defy the rise of entropy, and thus the laws of theuniverse.

“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 bequantified with what he called the information entropy. “In the 19th century, no one knew about information,” said TakahiroSagawa, a physicist at the University of Tokyo. “The modern understanding of Maxwell’s demon was established by Shannon’swork.”

The second vital piece of the puzzle was the principle of erasure. In 1961, the German American physicist Rolf Landauer showedthat any logically irreversible computation, such as the erasing of information from a memory, would result in a minimal nonzeroamount of work converted into heat dumped into the environment, and a corresponding rise in entropy. Landauer’s erasureprinciple 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 atcore an information-processing machine: It needed to record and store information about individual particles in order to decidewhen 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 theparticles. “You need to pay,” said Gonzalo Manzano, a physicist at the Institute for Quantum Optics and Quantum Information inVienna. The demon’s need to make room for more information inexorably led to a net increase in disorder.

Then in the 21st century, with the thought experiment solved, the real experiments began. “The most important development iswe can now realize Maxwell’s demon in laboratories,” said Sagawa.

In 2007 scientists used a light-powered gate to demonstrate the idea of Maxwell’s demon in action; in 2010, another teamdevised a way to use the energy produced by the demon’s information to coax a bead uphill; and in 2016 scientists applied theidea of Maxwell’s demon to two compartments containing not gas, but light.

“We switched the roles of matter and light,” said Vlatko Vedral, a physicist at the University of Oxford and one of the study’s co-authors. The researchers were ultimately able to charge a very small battery.

Others wondered if there might be less demanding ways to use information to extract useful work from a similar system. Andresearch published in February in Physical Review Letters seems to have found a way to do so. The work makes the demon into agambler.

The team, led by Manzano, wondered if there was a way to implement something like Maxwell’s demon but without theinformation requirements. They imagined a two-compartment system with a door, as before. But in this case, the door wouldopen and close on its own. Sometimes particles would randomly separate themselves into hotter and colder compartments. The

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demon could only watch this process and decide when to turn the system off. In theory this process could create a smalltemperature imbalance, and therefore a useful heat engine, if the demon was smart about when to end the experiment and lockany temperature imbalance in place, much as a smart gambler on a hot streak knows when to leave the table. “You can either playall night on the roulette table, or you can stop if you win $100,” said Édgar Roldán, a physicist at the International Center forTheoretical Physics in Italy who was a co-author on the study. “We’re saying we don’t need such a complicated device asMaxwell’s demon to extract work in the second law. We can be more relaxed.” The researchers then implemented such agambling demon in a nanoelectronic device, to show it was possible.

Ideas like this could prove useful in designing more efficient thermal systems, like refrigerators, or even in developing moreadvanced computer chips, which may be approaching a fundamental limit dictated by Landauer’s principle.

For the time being, though, our laws of the universe are safe, even when placed under the greatest scrutiny. What has changed isour understanding of information in the universe, and with it our appreciation of Maxwell’s demon, first a troublesome paradox,and now an invaluable concept — one that has helped to illuminate the remarkable link between the physical world andinformation.