Breaking the Law

Can quantum mechanics + thermodynamics = perpetual motion?

Hopeful inventors have for centuries tried to create machines that would run forever: gizmos such as wheels that turn unceasingly with no motor to drive them and engines that endlessly exploit the heat in the oceans to power ships.

Friction foils this optimistic 17th-century plan to both grind grain (M) and lift water. The downhill motion of water was supposed to drive the device. (Image from Georg Andreas Böckler, Theatrum machinarum novum, 1963) Courtesy of University of Kentucky Special Collections Library

The consequences of devising such perpetual motion machines would be wondrous because these tools would unleash energy without consuming fuel.

Despite the machines’ appeal, no one has ever succeeded in making one. Physicists attribute that miserable track record to the fact that the devices would defy fundamental laws of thermodynamics. Given that scientific lawlessness, most researchers don’t give perpetual motion half a thought.

Recently, however, several groups of scientists have taken a fresh look at the concept. They propose that the peculiarities of quantum mechanics permit what seem to be violations of one of the fundamental laws—at least on a microscopic scale.

Quantum theory, which stands out already for its bizarre consequences, describes the behavior of extremely small objects such as atoms and other elementary particles. If verified, the new findings in the realm of quantum thermodynamics might indicate that a certain class of perpetual motion machines is, in fact, possible.

Not surprisingly, these new proposals are getting a chilly reception from many physicists, even though one of the three recent theoretical reports appeared in the highly regarded journal Physical Review Letters (PRL). Skeptics note, for example, that the innovative arguments in favor of perpetual motion have yet to be put to the test in working devices. They also say that the theory behind the claim may have subtle, but fatal, flaws.

Two categories

Scientists divide perpetual motion schemes into two categories depending on whether they violate the first or second law of thermodynamics.

The first law says that energy can’t be created or destroyed.

The second law clamps a strong constraint on physical devices that do useful work by tapping the energy of something hot, like steam or burning fuel. The law requires that some energy must flow from one heat source to something else at a lower temperature. For example, a car engine must cough its exhaust heat into a cooler environment, not a hotter one. The take-home message of the second law is that not all of the heat source’s energy can go into doing work. Some must be wasted.

Perpetual motion schemes that rely on violations of the first law continue to be booed off stage by the scientific establishment. “This is something we don’t dare to do,” says theorist Theo M. Nieuwenhuizen of the University of Amsterdam.

Nevertheless, he adds, when he and a colleague probed the second law, they uncovered a route to feasible perpetual motion. Nieuwenhuizen and Armen E. Allahverdyan of CEA/Saclay in Gif-sur-Yvette, France, which is outside Paris, describe their work in the Aug. 28 PRL.

Testing the boundaries of the second law has been a sport for many physics luminaries including the late Richard P. Feynman. Each claim of a phenomenon that violates that law has stirred animated debate, and none has held up to scrutiny.

James Clerk Maxwell, the 19th-century scientific giant who came up with the theory of electromagnetism, offered a famous second-law challenge in 1867. He imagined a tiny being, a “demon,” who could observe and manipulate individual molecules and, by doing so, overthrow the second law (SN: 6/16/90, p. 378).

Here’s how: The imp could sit inside a gas-filled box that was divided by a partition with a small door in it. Because of random thermal fluctuations, some molecules in the gas would have more kinetic energy than others. The demon would open the door only to let the fastest molecules—those with the greatest kinetic energy—pass to the other side. That would transform what began as a uniform-temperature box into two sections at different temperatures—the second law’s prerequisite for accomplishing useful work, Maxwell reasoned.

Likewise, in their PRL report, Allahverdyan and Nieuwenhuizen come to what they themselves assess as an “appalling” conclusion: Useful work might emerge from a single heat reservoir as if one of Maxwell’s demons were at work. Although the researchers consider only an abstract mathematical model, they say their equations might apply to certain real-world systems of particles, albeit ones at a temperature close to absolute zero.

In each of their perpetual motion scenarios, a minuscule “test particle” interacts with a surrounding bath of other particles. Think of a dust speck in a droplet of water. Viewed under a microscope, the speck jiggles incessantly as it is constantly bombarded by water molecules—a phenomenon called Brownian motion. Allahverdyan and Nieuwenhuizen have analyzed a similar phenomenon that occurs on a much smaller scale.

Examples of their scenarios include an atom entering an extremely cold metal box filled with bouncing microwave photons or an electron injected into a frigid crystal filled with phonons, the vibrations of lattice atoms.

The researchers propose retrieving energy from those systems by pumping them with a smaller amount of energy. In the microwave case, they envision penetrating the box with a magnetic field having a strength that varies in a cyclical manner. For the crystal, a periodic variation in applied pressure could do the trick, Allahverdyan says.

If the particles in the system vibrate in a particular way, the energy can be recaptured, the researchers contend. The pattern needed to make this happen, known as an anharmonic vibration, requires that the speed of the vibrations depend on their size. The mathematical model indicates that the pumping would release more energy from the system than it would drive into it. And that opens the door to the coveted perpetual motion.

Foiled attempt

Various analysts have found that Maxwell’s demon would require energy to carry out his task, thereby foiling his attempt to circumvent the second law. “You have to feed the demon,” Nieuwenhuizen explains. Even a demon who scarcely moves a muscle to carry out his task would still need information about the molecules he sorts—and information is a form of energy, physicists have concluded.

Nieuwenhuizen and Allahverdyan, however, say that they’ve come across theoretical evidence for quantum systems that wouldn’t require the influx of energy that a demon would need. “Quantum mechanics is doing what the demon is supposed to do,” Nieuwenhuizen says, but quantum mechanics doesn’t need to be fed.

Here’s why. Classical physics portrays fundamental particles, such as atoms and electrons, as tiny billiard balls. Quantum mechanics, on the other hand, also represents them as waves. According to that wave nature, elementary particles extend across space and interact with each other through the overlapping of their crests and troughs.

The extended interaction, known as quantum coherence, gives quantum systems their remarkable character. It permits electrons to flow without resistance through superconductors and superfluid helium to mysteriously climb out of a cup of its own accord.

In the systems that they consider, Allahverdyan and Nieuwenhuizen stipulate that the extended interactions between particles be strong enough that another even stranger type of interaction, known as entanglement, also takes place. Entangled particles share a single quantum state, so that whatever happens to one immediately affects the other, even if they are widely separated (SN: 11/20/99, p. 334:

A jolt of energy injected into a classical heat bath—as would happen by, say, dropping hot coals into a swimming pool—quickly peters out into random motions of molecules, slightly raising the bath’s temperature. As the so-far universal failure of Maxwell’s demon shows, once the energy has dissipated, the process can’t be reversed.

In the systems studied by Allahverdyan and Nieuwenhuizen, however, quantum coherence and entanglement keep the energy accessible. It roams incessantly among the particles and waves. For example, when an atom enters a microwave cavity—or an electron penetrates a lattice—it joins in a back-and-forth exchange of energy and momentum.

With all that quantum-scale activity going on, the researchers asked whether thermodynamics theory—including its second law—could be applied to these systems. One prerequisite for using thermodynamics theory is that the system should settle down to a balanced, unchanging state, an equilibrium, at a slightly higher temperature. But, that’s not happening in their model.

So, they conclude that thermodynamics doesn’t apply. They argue that their theoretical system doesn’t actually violate the second law; the violation is only “apparent.” Yet they hold that their system still achieves what has long been considered impossible—it wangles useful work out of a single heat reservoir.

“The point with perpetual motion is whether you can work with one reservoir,” Nieuwenhuizen remarks. “Here, we have a case where that is possible.”

Quantum route

Two other scientific reports in the past year also argue for a quantum route to perpetual motion. In one, Alexey V. Nikulov of the Russian Academy of Sciences’ Institute of Microelectronics Technology and High Purity Materials in Chernogolovka, which is near Moscow, focuses on a hollow ring of deeply chilled superconducting material with electrons circulating in its walls. By switching superconductivity on and off in a segment of the ring, Nikulov argues, random thermal fluctuations would generate a useful voltage thereby violating the second law.

In the other report, theorists Vladislav Cápek and Jiri Bok, both of Charles University in Prague, the Czech Republic, propose that violations might take place even in room-temperature interactions, say, between ions and biomolecules. Indeed, Cápek told Science News, those breakdowns of the second law might already be occurring in living systems.

There’s a caveat that applies to all three reports. None actually claims to make truly perpetual motion possible. If the first law could be violated, a machine could operate forever. However, a perpetual motion machine of the second type—a second-law violator—is powered by the kinetic energy of the reservoir. So, the machine’s motion would stop when the bath’s temperature hits absolute zero, just as an engine running out of gas would stop. This means that the motion of such a machine wouldn’t be perpetual after all.

Neither the Russian nor Czech work was published prominent venues such as PRL. The work of Cápek and Bok appeared in the December 1999 Czech Journal of Physics. Nikulov’s study hasn’t been published; it’s posted to the physics preprint server on the Internet (

How does a perpetual motion claim get into the austere, international, and highly respected Physical Review Letters? According to Gene Wells, one of the journal’s editors, the quantum world remains so puzzling that the editor of the Allahverdyan-Nieuwenhuizen submission didn’t balk. “As long as [the proposed second-law violation] is in that quantum regime, I’m not that troubled,” Wells says.

After all, even the sacred first law’s conservation of energy breaks down in the quantum realm, albeit in a limited way, he notes. That’s because Heisenberg’s uncertainty principle allows energy momentarily to appear from nothing, although it must be quickly paid back.

However, any perpetual motion schemes based on classical physics would trouble Wells. “If [the analysis] were purely classical, we, of course, would suspect it and may not even send it out to be reviewed,” he says.

Not buying it

Although stating their case in PRL gives Allahverdyan and Nieuwenhuizen clout, many thermodynamics specialists still aren’t buying their arguments. “Such breakthroughs have happened in science before,” confesses Bjarne Andresen of the University of Copenhagen, “but I do not believe that this is another one.”

Quantum information theorist Barbara M. Terhal of IBM T. J. Watson Research Center in Yorktown Heights, N.Y., notes that Allahverdyan and Nieuwenhuizen are working with a mathematical entity, not actual physical systems. “If they did a more careful analysis based on the physics,” she ventures, “they would see nothing going on.”

Physical chemist John Ross of Stanford University isn’t ready to draw any conclusions, but he’s not expecting much. “It’s easy to say foolish things about thermodynamics, and some very wise people have said foolish things,” he cautions.

Others, however, feel that the new research may be on a promising path. “The violation of the second law at very low temperatures for certain systems is real,” says Mikhail Anisimov of the University of Maryland in College Park.

William G. Unruh of the University of British Columbia in Vancouver explains that a decade ago, he and other physicists came upon the same quantum phenomenon that Allahverdyan and Nieuwenhuizen are probing, but the earlier workers didn’t claim the possibility of perpetual motion. However, the new research goes further than the early work by, for instance, examining anharmonic vibration, Unruh points out.

Nonetheless, he comments, “my strong suspicion is that the amount of energy you have to stick in . . . is as much energy as you get out.”

Igor M. Sokolov of the University of Freiburg in Germany thinks the PRL authors are onto something, though not necessarily a breakdown of the second law. They may have discovered unnoticed flaws in the mathematical tools used to describe quantum systems, he says.

On the other hand, if they’re right about perpetual motion, “it could give rise to a couple of Nobel prizes,” he muses.

Dramatic impact

If verified, any second-law violations would almost certainly have a dramatic impact on the scientific world. However, the practical consequences of these reports could still prove minuscule.

Nikulov has already calculated the power that each of his proposed superconductive rings would generate. The device “cannot solve the energy problem. Its power is very weak,” he concludes. Nonetheless, systems made up of many rings would generate enough energy to serve as direct-current sources in low-power circuits or to run microscopic refrigeration systems, he argues.

Nieuwenhuizen says that he’s given little thought to harnessing the unusual proposed energy source or how much energy it might provide. Perhaps the technique would provide a way to cool also-hypothetical quantum computers, Allahverdyan suggests.

None of these possible applications seem like much by the standards of 19th-century dreamers and their hopes of seawater-powered, transoceanic voyages. In the thermal fluctuations of a heat bath that’s already nearly at absolute zero, there’s too little energy for those visions. There’s only enough, Nieuwenhuizen concedes, so that “a little quantum boat could cross a little quantum ocean.”

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