Ultrasmall engines bend second law of thermodynamics

When French engineer Sadi Carnot calculated the maximum efficiency of a heat engine in 1824, he had no idea what heat was. In those days, physicists thought heat was a fluid called caloric. But Carnot, later lauded as a pioneer in establishing the second law of thermodynamics, didn’t have to know those particulars, because thermodynamics is insensitive to microscopic details. Heat flows from hot to cold regardless of whether it consists of a fluid or, as it turns out, the collective motion of trillions of trillions of molecules. Thermodynamics, the laws and equations governing energy and its usefulness to do work, concerns itself only with the big picture.

It’s a successful approach. As thermodynamics requires, energy is always conserved (the first law), and when it flows from hot to cold it can do work, limited by the generation of disorder, or entropy (the second law). These laws dictate everything from the miles per gallon a car engine gets to the battery life of a smartphone. They help physicists better understand black holes and why time moves forward but not backward (SN: 7/25/15, p. 15).

Yet the big picture approach, considering the forest rather than the trees, has made physicists wonder if thermodynamics holds at all scales. Would it work if an engine consisted of three molecules rather than the typical trillion trillion? In the realm of the very small, governed by the quirky rules of quantum mechanics, perhaps the thermodynamic code is not so rigid.

“Thermodynamics was designed for big stuff,” says Janet Anders, a theoretical physicist at the University of Exeter in England. “We haven’t really integrated thermodynamics with quantum mechanics.”

Over the last few decades, physicists have gradually explored heat flow at the quantum level, intrigued by the possibility of finding violations of thermodynamics’ second law. So far, the second law has held strong. But new precision experimental techniques are allowing physicists to explore the quantum foundations of thermodynamics more fully. Testing the limits set by theorists, researchers are building tiny engines, some powered by a single atom, and measuring the devices’ feeble oomph.

Even if physicists can’t break the thermodynamic rules, recent evidence suggests ways to bend them — especially by exploiting the way quantum entanglement weaves together the fates of a few particles. Techniques used in processing quantum information could prove useful for squeezing extra energy out of miniature engines, for instance. These lessons could help scientists build nanomachines that harvest heat and use it to deliver medicine inside the body, or help reduce energy loss in the tiny components of traditional computers.

Quantum engines

Any future practical applications of this work will depend on understanding how basic thermodynamic principles operate at ultrasmall scales.

It goes back to statistics, says University College London quantum theoretical physicist Jonathan Oppenheim. If the trillion trillion gas molecules in a steam engine were represented by that many coins, then the result of flipping all those coins would be a homogenous mixture of heads and tails, the equivalent of stable temperature and maximum entropy. That’s why steam engines always follow the rules. But flip three minicoins inside a tiny quantum engine and all three could easily land on heads, as if all the fast molecules stayed in one compartment rather than mixing with the other — a violation of the second law.

Experiments over the years had suggested that if the second law of thermodynamics does break down at small scales, the violation is not very drastic. Last year, Oppenheim and colleagues got more specific, publishing a detailed analysis in the Proceedings of the National Academy of Sciences. Their results indicate that not only does the second law actually hold at the quantum scale, it is also more demanding.

Rather than analyzing entropy directly, Oppenheim’s team looked at how much energy a system has available to do work, a quantity called free energy. In our macroscopic world, the amount of free energy depends only on a system’s temperature and entropy. But by zooming in toward smaller and smaller collections of particles, the researchers found that they had to take into account several more varieties of free energy. Every one of them decreases over time. In other words, the second law requires adherence to even more rules at the quantum level.

Recent experiments have made it clear that attempts to circumvent the second law at any scale are doomed. In the Dec. 31 Physical Review Letters, Jonne Koski, a physicist at Aalto University in Finland, and colleagues created the laboratory equivalent of the heat-manipulating “demon” conjured by Scottish physicist James Clerk Maxwell in 1867.

Maxwell wondered whether a hypothetical microscopic entity tracking the particles flitting around two adjacent containers could separate the fast-moving particles from the slow ones. The demon’s actions would minimize the system’s total entropy, a violation of the second law, and create a temperature difference that could be exploited to do work for free.

Koski’s team built a demonic device that deprived an electronic circuit of heat and thus its entropy as well. The demon did its job: A visitor to the lab observing the experiment would think  the circuit was violating the second law. But the researchers also noticed that the demon paid a price for its transgressions. As it performed its dirty deed, the demon itself heated up. The total entropy of the circuit and the demon together actually increased, just as the second law requires (SN Online: 12/1/15).

Koski’s electronic demon failed because of its reliance on information about individual particles. The connection between information and thermodynamics dates back to 1929. That’s when Hungarian physicist Leo Szilard dug deeper into Maxwell’s thought experiment and drew up a blueprint for exploiting information about particles, such as their position and velocity, to perform tasks. Szilard’s work demonstrated that in physics, information isn’t merely a stock quote or a baseball player’s batting average — it’s physical.

More than three decades later, IBM physicist Rolf Landauer showed that Szilard’s approach came with a cost. Maxwell’s demon may capitalize on its knowledge about one particle, Landauer said, but the demon must use up the energy it gained when it scrubs that information from its finite memory and turns its attention to the next particle. Erasing information costs energy. That’s why the sophisticated demonic circuit failed to circumvent the second law.

Information is clearly important for understanding thermodynamics, and it’s also downright essential for making sense of the stranger parts of quantum mechanics. Tiny bits of matter can essentially exist in two places at once, a phenomenon called superposition. Two or more particles can be wrangled into what’s known as an entangled state, intricately linking the particles’ properties regardless of the distance between them.

Many physicists are trying to exploit superposition, quantum entanglement and other quantum trickery to perform information-heavy tasks that are impossible under the rules of classical physics. Researchers envision supersecure communication networks and quantum computers that exploit entangled photons or ions to solve complex problems with ease (SN: 11/20/10, p. 22).

But information means much more than just exchanging and processing 1s and 0s. As a result, physicists pondering quantum computing and communication have turned their attention to thermodynamics. They’ve begun asking whether properties such as entanglement could also offer an advantage in converting heat into work.

In the October–December 2015 Physical Review X, a European team demonstrated that a system of several entangled particles stores more usable energy than the same particles without quantum connections. The advantage, which quickly disappears as the number of particles increases, boils down to the notion that information is a resource. Entangled particles essentially provide information for free, because knowing something about one particle reveals something about its entangled partners (SN: 1/9/16, p. 9).

Even though the second law holds strong, says study coauthor Marcus Huber, the ability to exploit information from quantum effects “also helps you to do things that you couldn’t do classically.”

Information advantage

Obtaining information at a discount may enable technology that bends the second law and outperforms the best life-size engines. “What we can hope for are machines that run faster, refrigerators that get cooler or batteries that store more or charge faster,” says Huber, a quantum information theorist at the University of Geneva.

Huber compares the challenge ahead to playing a game, much like the one Carnot played in the 19th century. Carnot essentially turned dials controlling variables such as temperature and pressure until he had squeezed the maximum efficiency out of a steam engine. Today’s physicists have different goals — perhaps creating a microscopic refrigerator to cool their instruments to unfathomably low temperatures. To achieve such goals, physicists plan to turn the dials for variables like entanglement and see what happens.

Soon scientists may be able to start playing those games with engines exploiting quantum effects in the lab. German researchers took a step toward that goal in October by building a heat engine consisting of a single atom. Johannes Roßnagel, a quantum physicist at the University of Mainz, and colleagues built a cone-shaped enclosure around a calcium ion. After using a laser and electric field to heat up the ion to about one degree above absolute zero, the researchers measured the work performed by the ion as it exerted a subtle push toward the top of the cone.

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The nanoscopic engine worked just as the laws of thermodynamics say it should, the researchers reported in a paper posted online at arXiv.org. Adjusting for the tiny weight of the ion, the power was comparable to that of a car engine, Roßnagel says. “It’s quite interesting to see that you can drive heat machines with a single atom,” he says.

Despite the measureable power output of the single-ion engine, Roßnagel warns that nano-sized engines for practical use are decades away at best. Instead, the usefulness of quantum thermo-dynamics will probably happen under the hood of other technologies.

Some researchers have their eyes on the multi-billion-dollar computer chip industry. In the drive to build ever-faster computers, engineers keep shrinking transistors to pack more and more onto chips. The transistors, some just tens of nano-meters wide, tend to leak electrons and heat up. That heat ruins the energy efficiency of the computer and damages components. Quantum thermodynamics could help physicists learn tricks to reduce the amount of wasted heat or perhaps even harvest it with small devices inside the computer.

Heat management is even more crucial for physicists seeking to build practical quantum computers. Such a device needs to operate at extremely low temperatures to exploit quantum effects and potentially outperform traditional computers.

Next, Roßnagel and his colleagues plan to chill their single atom until it’s capable of maintaining delicate quantum states including superposition and entanglement. Such an experiment would put Huber’s theoretical results to the test and expose the potential of adjusting those “quantumness” knobs to better exploit heat to do work.

A few contrarians in the physics community say that such experiments could finally violate the vaunted second law of thermodynamics. But don’t bet on it. Early 20th century English astrophysicist Arthur Eddington is still looking good with his prediction that any theory attempting to defy the second law will “collapse in deepest humiliation.” But he didn’t say anything about moving the goalposts a bit.

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This article appears in the March 19, 2016 issue with the headline, “The laws of heat go small: Physicists explore thermodynamics in the quantum realm.”