Illustration of Maxwell’s Demon. Credit: Jason Torchinsky.

Maxwell’s Demon Meets Quantum Dots

By Jennifer Ouellette | February 18, 2013

Entropy. It’s at the root of one of the most famous physics thought experiments of the 20th century (second only to the infamous Schroedinger’s cat), devised by a Scottish physicist named James Clerk Maxwell, called Maxwell’s Demon. And now scientists at the Institute of Technology in Berlin have devised a nanoscale version of that thought experiment using quantum dots.

Entropy is better known as the second law of thermodynamics. Not only can you not have a closed system that puts out more energy than you consume, but you’re always going to lose a little bit of energy in the energy conversion process. One of the neat things about thermodynamics is that if you can create a large enough differential between potential and kinetic energy — for example, a big difference in temperature between two compartments — you’ve got yourself a handy energy source.

Refrigerators work on this simple concept, known as the Carnot cycle. Gas (usually ammonia) is pressurized in a chamber, said pressure causes that gas to heat up, this heat is then dissipated by coils on the back of the appliance, and the gas condenses into a liquid. It’s still highly pressurized, sufficiently so that the liquid flows through a hole to a second low-pressure chamber. That abrupt change in pressure makes the liquid ammonia boil and vaporize into a gas again, also dropping its temperature — thereby keeping your perishable foodstuffs nicely chilled. The cold gas gets sucked back into the first chamber, and the entire cycle repeats ad infinitum — or at least as long as the appliance is plugged in.

That’s the catch. The refrigerator is not a truly “closed system”: it gets a constant influx of energy from the wall outlet that enables it to operate continuously. Left on its own, without that crucial influx, and the interior would cease to be nicely chilled, and all the food therein would perish. Because entropy always increases in the end.

The second law of thermodynamics is frankly pretty unyielding. But while it can’t be broken, perhaps it can be bent by a cunning infusion of energy that escapes detection by all but the most perceptive eye. James Clerk Maxwell proposed the most famous evasion of thermodynamics back in 1871.

Maxwell is best known for formulating his famed equations for electromagnetism that are still in use today. But he was equally fascinated by thermodynamics, notably the fact that heat cannot flow from a colder to a hotter body. And one day Maxwell had an idea: what if hot gas molecules merely had a high probability of moving toward regions of lower temperature?

He envisioned an imaginary, tiny creature (Maxwell’s Demon) who could wring order out of disorder to produce energy by making heat flow from a cold compartment to a hot one, creating that all-important temperature difference. The imp guards a hypothetical pinhole in a wall separating two compartments of a container filled with gas — similar to the two chambers in a refrigerator — and can open and close a shutter that covers the hole whenever it wishes.

The gas molecules in both compartments will be pretty disordered, with roughly the same average speed and temperature (at least at the outset), so there’s very little energy available for what physicists call “work”: defined as the force over a given distance (W=fd) It means that you’ll spend the same amount of energy carrying a heavy load over a short distance, as you will carrying a feather over a very long distance.

In Maxwell’s thought experiment, the atoms start out in a state of thermodynamic equilibrium. But they’re still jiggling around, as atoms are wont to do, so over time, there are small fluctuations as some atoms start moving more slowly or more quickly than others. Of course, balance will soon be restored, since the excess heat will be transferred from hotter to colder molecules until they are all once again in equilibrium.

Ah, but then Maxwell’s little demon interferes. Whenever it spots a molecule moving a bit faster in the right compartment and start to move towards the pinhole, he opens the shutter just for a moment so it can pass through to the left side. It does the same for slower molecules on the left side, letting them pass to the right compartment.

So the molecules in the left compartment get progressively hotter, while those on the right side get colder. The creature creates a temperature difference, and once you have that, well, it’s a trivial matter to harness that difference for work. Entropy has been outwitted — or so it would seem.

In reality, Maxwell’s thought experiment was a trick question. It’s statistically impossible to sort and separate billions of individual molecules by speed or temperature; Nature just doesn’t do this. You can’t throw a glass of water into the sea and expect to get back the exact same glass of water, right down to the last single molecule.

Okay, hypothetically you might be able to do this, provided you knew the exact speeds and positions of each and every molecule (at the quantum level, this is an impossibility thanks to the Uncertainty Principle). But you’d have to expend a huge amount of energy to collect that detailed information, far more than the energy you’d get out of the system once you’d succeeded in creating the crucial temperature difference.

Just like the refrigerator, Maxwell’s mischievous little imp also requires energy to operate. There is no such thing as a perfect heat engine; you’ll always lose some heat in the process. The second law of thermodynamics is the bane of every researcher striving to develop alternative energy sources, and they have to be cost-competitive as well as energy-efficient.

Read more: Maxwell’s Demon Meets Quantum Dots | Cocktail Party Physics, Scientific American Blog Network.

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