February 18, 2013 | 1
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. [Clarification for certain grouchypants readers who missed the broader context of this post: technically the energy isn't "lost," it's converted to heat, a highly disordered form of energy that isn't useful for work. Since the whole point of Maxwell's Demon is to demonstrate how to get usable energy -- i.e., work -- from a state of thermal equilibrium, for practical purposes, that energy is "lost" because it isn't usable. The total amount of energy is conserved, however.]
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.
That hasn’t kept physicists from playing around with the concept of Maxwell’s Demon experimentally in the ensuing 130+ years. Back in 2007, there was a nifty manmade molecular machine created by another Scotsman, David Leigh, and his colleagues at the University of Edinburgh. Most biological processes involve driving chemical systems away from thermal equilibrium, so Leigh devised a chemical “information ratchet” that performs much the same role as Maxwell’s hypothetical demon: creating a temperature difference out of thermal equilibrium, thereby seemingly “reversing” entropy.
In 2008, Daniel Steck of the University of Oregon in Eugene built a laser barrier set-up in which the beam lets atoms pass through only in one direction, such that they all eventually end up on a single side, chilled to extremely low temperatures. Steck created a “box” out of laser light/electromagnetic fields, and then added two parallel lasers that together serve as the “trapdoor.” The beam on the right is the barrier, and the one of the left is the “demon,” responsible for the “sorting.”
And in 2010, physicists at the University of Tokyo built a nanoscale experiment in which a bead was coaxed up a spiral staircase without any energy being directly transferred to the bead to accomplish the feat. Per Nature: “Instead, it is persuaded along its route by a series of judiciously timed decisions to change the height of the ‘steps’ around it, based on information about the bead’s position.” So in some sense, information is being converted to energy. I’ll let Sean Carroll (a.k.a. the Time Lord) explain:
The idea is called Szilárd’s Engine. … [I]t’s a box of gas with just one particle, moving in one dimension. (In the real experiment, they used knowledge of a particle’s position to make it hop up a staircase.) The equivalent of “maximum entropy” here is “we have no idea where the particle is.” There is energy in the box, equal to kT/2, but we can’t get it out.
But now imagine that someone gives us one bit of information: they tell us which side of the box the particle is on. Now we can get some energy out! All we have to do is wait until the particle is on the left-hand side of the box, and quickly slip in our piston coming out the right. The particle will now bump into the piston, pushing it to the right, allowing us to useful work, like lifting a very tiny bucket or something. In the process some of the particle’s energy is transferred to the piston, so we’ve extracted some energy from the box. Note that we could not have done this if we hadn’t been given the information — without knowing where the particle is, our piston would have lost energy on average just as often as it gained energy, so we couldn’t have done any useful work.
Which brings us to the latest work by the German physicists. Quantum dots are tiny bits of semiconductors just a few nanometers in diameter. It’s like taking a wafer of silicon and cutting it in half over and over again until you have just one tiny piece with about a hundred to a thousand atoms. That’s a quantum dot. Billions of them could fit on the head of a pin.
The physicists proposed that one could physically build the experimental equivalent of Maxwell’s Demon on the nanoscale with a pair of interacting quantum dots. One dot is the demon, and is connected to a pair of thermal reservoirs, making it, in effect, a single-electron transistor.
The other dot represents the controlled system and is coupled to another reservoir. One of the most useful properties of quantum dots is that they can be tuned to specific wavelengths. So it should be possible to tune the second dot in such a way that it can tell if the first dot is in either a o or 1 state — you just need to ensure both dots are interconnected.
If you think of the two dots as glasses, if they were perfectly correlated, when the first glass was empty, the second would be full, and vice versa. The end result of the process is roughly the equivalent of gaining extra information from the production of entropy.
While there is an increase in the total entropy — per the second law of thermodynamics — that increase doesn’t occur in the demon-y quantum dot by itself. As one of the collaborators, Massimiliano Esposito (University of Luxembourg) told Phys.org: “It does, of course, respect thermodynamics…. However, if the part of the system implementing the demon is disregarded, everything looks as if the remaining pat of the system was subjected to a Maxwell demon breaking the second law while keeping the first one intact.”
Granted, they haven’t actually built such an experiment, but the researchers are optimistic that it should be possible. So Maxwell’s Demon need not be all that smart, or even sentient — just very well designed.
Jarzynski, C. (1997) “Nonequilibrium Equality for Free Energy Differences,” Physical Review Letters 78: 2690-2693.
Maxwell, J. C. (1871). Theory of Heat, reprinted. New York: Dover, 2001.
Serreli V., et al. (2007) Nature 445: 523 – 527.
Strasberg, Philip et al. (2013) “Thermodynamics of a Physical Model Implementing a Maxwell Demon,” Physical Review Letters 110: 040601.
Thorn, Jeremy J. et al. (2008) “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Physical Review Letters 100, 240407.
Toyabe, Shoici et al. (2010) “Information Heat Engine: Converting Information to Energy by Feedback Control,” Nature Physics 6: 988-992.
[Partially adapted from a June 2008 post at the old archived Cocktail Party Physics blog.]