People have learned to build very powerful internal combustion engines, but have not learned the main thing - to significantly increase their efficiency. The limit on this path is set by the second law of thermodynamics, which states that the entropy of a system inevitably increases. But is it possible to overcome this limit with the help of quantum physics? It turned out that it is possible, but for this it was necessary to understand that entropy is subjective, and heat and work are far from the only possible forms of energy. For more information on what quantum engines are, how they are arranged and what they are capable of, read our material.
Over 300 years of development of technology for calculating, designing and designing engines, the problem of creating a machine with a high efficiency factor has not been solved, although it is critical for many areas of science and technology.
Quantum physics, discovered at the beginning of the 20th century, has already presented us with many surprises in the world of technology: atomic theory, semiconductors, lasers and, finally, quantum computers. These discoveries are based on the unusual properties of subatomic particles, namely, quantum correlations between them - a purely quantum way of exchanging information.
And it seems that quantum physics is ready to surprise us again: years of development of quantum thermodynamics have allowed physicists to show that quantum heat engines can have high efficiency on small scales, inaccessible to classical machines.
Let's take a look at what quantum thermodynamics is, how heat engines work, what improvements quantum physics gives, and what needs to be done to create an efficient engine of the future.
Classic heat engines
In his 1824 book, Reflections on the Motive Force of Fire, 28-year-old French engineer Sadi Carnot figured out how steam engines can efficiently convert heat into work that makes a piston move or a wheel turn.
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To Carnot's surprise, the efficiency of an ideal engine depended only on the temperature difference between the engine's heat source (a heater, usually a fire) and a heat sink (a refrigerator, usually ambient air).
Carnot realized that work is a by-product of the natural transition of heat from a hot to a cold body.
The scheme of work of the heat engine.
In heat engines, the following cycle is used. Heat Q 1 is supplied from the heater with temperature t 1 to the working fluid, part of the heat Q 2 is removed to the refrigerator with temperature t 2, t 1> t 2.
The work done by the heat engine is equal to the difference between the supplied and removed heat: A = Q 1 - Q 2, and the efficiency η will be equal to η = A / Q 1.
Carnot showed that the efficiency of any heat engine cannot exceed the efficiency of an ideal heat engine operating in its cycle with the same temperatures of the heater and refrigerator ηCarnot = (t 1 - t 2) / t 1. Creating an efficient heat engine is the maximum approximation of the real Efficiency η to ideal ηCarnot.
Sadi Carnot died of cholera eight years later - before he could see how, already in the 19th century, his formula for efficiency turned into the theory of classical thermodynamics - a set of universal laws linking temperature, heat, work, energy and entropy.
Classical thermodynamics describes the statistical properties of systems by reducing microparameters, such as the positions and velocities of particles, to macroparameters: temperature, pressure, and volume. The laws of thermodynamics turned out to be applicable not only to steam engines, but also to the Sun, black holes, living things and the entire Universe.
This theory is so simple and general that Albert Einstein believed that it "will never be overthrown." However, from the very beginning, thermodynamics occupied an extremely strange position among other theories of the universe.
“If physical theories were human, thermodynamics would be a village witch,” wrote physicist Lydia del Rio a few years ago. "Other theories find her strange, different from the rest, but everyone comes to her for advice and no one dares to contradict her."
Thermodynamics has never claimed to be a universal method for analyzing the world around us; rather, it is a way to effectively use this world.
Thermodynamics tells us how to make the most of resources like hot gas or magnetized metal to achieve specific goals, be it moving a train or formatting a hard drive.
Its versatility comes from the fact that it does not try to understand the microscopic details of individual systems, but only cares about determining which operations are easy to implement in these systems and which are difficult.
This approach may seem strange to scientists, but it is actively used in physics, computer science, economics, mathematics and many other places.
One of the strangest features of a theory is the subjectivity of its rules. For example, a gas made up of particles with the same temperature on average has microscopic temperature differences upon closer inspection.
In recent years, a revolutionary understanding of thermodynamics has emerged, explaining this subjectivity through quantum information theory, which describes the propagation of information through quantum systems.
Just as thermodynamics originally grew out of attempts to improve steam engines, modern thermodynamics describes the operation of already quantum machines - controlled nanoparticles.
For a correct description, we are forced to extend thermodynamics to the quantum region, where concepts such as temperature and work lose their usual meaning, and the classical laws of mechanics cease to work.
Quantum thermodynamics
The birth of quantum thermodynamics
In a letter from 1867 to his Scottish colleague Peter Tate, the famous physicist James Clark Maxwell formulated the famous paradox, hinting at the connection between thermodynamics and information.
The paradox concerned the second law of thermodynamics - the rule that entropy always increases. As Sir Arthur Eddington later noted, this rule "occupies a dominant position among the laws of nature."
According to the second law, energy becomes more disordered and less useful as it travels from hot to cold bodies and the differences in temperature decrease.
And as we remember from Carnot's discovery, a hot and cold body is required to do useful work. The fires go out, the morning coffee cups cool down, and the universe rushes towards a state of uniform temperature known as the heat death of the universe.
The great Austrian physicist Ludwig Boltzmann showed that the increase in entropy is a consequence of the laws of ordinary mathematical statistics: there are many more ways to evenly distribute energy between particles than for its local concentration. When particles move, they naturally tend to higher entropy states.
But Maxwell's letter described a thought experiment in which a certain enlightened being - later called Maxwell's demon - uses his knowledge to reduce entropy and violate the second law.
The almighty demon knows the position and speed of every molecule in a container of gas. By dividing the container into two halves and opening and closing the small door between the two chambers, the demon lets only fast molecules in one direction and only slow ones in the other.
The demon's actions divide the gas into hot and cold, concentrating its energy and reducing the total entropy. A once useless gas with a certain average temperature can now be used in a heat engine.
For many years, Maxwell and others wondered how the law of nature could depend on knowing or not knowing the position and speed of molecules. If the second law of thermodynamics is subjectively dependent on this information, then how can it be absolute truth?
Relationship of thermodynamics to information
A century later, the American physicist Charles Bennett, drawing on the work of Leo Szilard and Rolf Landauer, resolved the paradox by formally linking thermodynamics to the science of information. Bennett argued that the demon's knowledge is stored in his memory, and the memory must be cleared, which requires work.
In 1961, Landauer calculated that at room temperature, a computer needs at least 2.9 x 10-21 joules to erase one bit of stored information. In other words, when the demon separates hot and cold molecules, reducing the entropy of the gas, his consciousness consumes energy, and the total entropy of the gas + demon system increases without violating the second law of thermodynamics.
Research has shown that information is a physical quantity - the more information you have, the more work you can extract. Maxwell's demon creates work from gas at one temperature, because he has much more information than an ordinary observer.
It took another half century and the heyday of quantum information theory, a field born of the pursuit of the quantum computer, for physicists to study in detail the startling implications of Bennett's idea.
Over the past decade, physicists have assumed that energy travels from hot objects to cold objects due to a certain way of propagating information between particles.
According to quantum theory, the physical properties of particles are probabilistic and particles can be in a superposition of states. When they interact, they become entangled by combining together the probability distributions describing their states.
The central position of quantum theory is the statement that information is never lost, that is, the present state of the Universe retains all information about the past. However, over time, as the particles interact and become more and more entangled, information about their individual states is mixed and distributed among more and more particles.
The cup of coffee cools down to room temperature, because when coffee molecules collide with air molecules, the information that encodes the coffee energy leaks out, is transmitted to the surrounding air and is lost in it.
However, understanding entropy as a subjective measure allows the Universe as a whole to develop without loss of information. Even when the entropy of parts of the Universe, for example, gas particles, coffee, N + 1 readers, grows as their quantum information is lost in the Universe, the global entropy of the Universe always remains zero.
Quantum heat engines
How, now, using a deeper understanding of quantum thermodynamics, to build a heat engine?
In 2012, the Technological European Research Center for Quantum Thermodynamics was established and currently employs over 300 scientists and engineers.
The center's team hopes to investigate the laws governing quantum transitions in quantum motors and refrigerators that might someday cool computers or be used in solar panels, bioengineering, and other applications.
Researchers already understand much better than before what quantum engines are capable of.
A heat engine is a device that uses a quantum working fluid and two reservoirs at different temperatures (heater and cooler) to extract work. Work is the transfer of energy from the engine to some external mechanism without changing the entropy of the mechanism.
On the other hand, heat is the exchange of energy between the working fluid and the reservoir, which changes the entropy of the reservoir. With a weak connection between the reservoir and the working fluid, heat is related to temperature and can be expressed as dQ = TdS, where dS is the change in the reservoir entropy.
In an elementary quantum heat engine, the working fluid consists of one particle. Such a motor satisfies the second law and is therefore also limited by the Carnot efficiency limit.
When the working medium is brought into contact with the reservoir, the population of the energy levels changes in the working medium. The defining property of the reservoir is its ability to bring the working fluid to a given temperature, regardless of the initial state of the body.
In this case, temperature is a parameter of the quantum state of the system, and not a macroparameter, as in classical thermodynamics: we can speak of temperature as the population of energy levels.
In the process of energy exchange with the reservoir, the body also exchanges entropy; therefore, energy exchange at this stage is considered as heat transfer.
For example, consider the quantum Otto cycle, in which a two-level system will act as a working fluid. In such a system, there are two energy levels, each of which can be populated; let the energy of the ground level be E 1, and the excited level E 2. The Otto cycle consists of 4 stages:
I. The distance between the levels E 1 and E 2 increases and becomes Δ 1 = E 1 - E 2.
II. There is contact with the heater, the system heats up, that is, the upper energy level is populated and the entropy of the working fluid changes. This interaction lasts time τ 1.
III. There is a compression between the levels E 1 and E 2, that is, there is work on the system, now the distances between the levels are Δ 2 = E 1 - E 2.
IV. The body is brought into contact with the refrigerator for a time τ 2, which gives it the opportunity to relax, to empty the upper level. The lower level is now fully populated.
Here we can say nothing about the temperature of the working fluid, only the temperatures of the heater and refrigerator matter. The perfect work can be written as:
dW = (p 0 (τ 1) - p 1 (τ 2)) (Δ 1 - Δ 2), (1)
where p 0 (1) is the probability that the working fluid was in the ground (excited) state. The efficiency of this quantum four-stroke engine is η = 1 - Δ 1 / Δ 2.
Otto cycle on a quantum two-level system.
For example, it is possible to build a quantum engine in which a superconducting qubit plays the role of a working fluid, and two normal resistors with different resistances are used as a heater and a refrigerator.
These resistors generate noise that has a characteristic temperature: big noise - heater, small - refrigerator.
The correct operation of such an engine was shown in the work of scientists from Aalto University in Finland.
In the implementation of the Otto cycle, the difference between the energy levels can be modulated by a constant magnetic flux, that is, "squeeze" or "expand" the levels, and switching on the interaction with the reservoirs was perfectly obtained by short microwave signals.
In 2015, scientists at the Hebrew University of Jerusalem calculated that such quantum motors could outperform classical counterparts.
These probabilistic engines still follow the Carnot formula for efficiency in terms of how much work they can extract from the energy passing between hot and cold bodies. But they are able to retrieve work much faster.
A single-ion engine was experimentally demonstrated and presented in 2016, although it did not use quantum effects to amplify power.
Recently, a quantum heat engine based on nuclear magnetic resonance was built, whose efficiency was very close to the ideal ηCarnot.
Quantum heat engines can also be used to cool both large and microscopic systems, such as qubits in a quantum computer.
Cooling a microsystem means decreasing populations at excited levels and decreasing entropy. This can be done through the same thermodynamic cycles involving the heater and refrigerator, but running in the opposite direction.
In March 2017, an article was published in which, using quantum information theory, the third law of thermodynamics was derived - a statement about the impossibility of reaching absolute zero temperature.
The authors of the article showed that the limitation of the cooling rate, which prevents the achievement of absolute zero, arises from the limitation on how quickly information can be pumped out of particles in an object of finite size.
The speed limit has a lot to do with the cooling capabilities of quantum refrigerators.
The future of quantum engines
Soon we will see the heyday of quantum technologies, and then quantum heat engines can help a lot.
It will not work to use a kitchen refrigerator to cool microsystems due to its erratic operation - on average, the temperature in it is low, but locally it can reach unacceptable values.
Due to the close connection of quantum thermodynamics with information, we are able to use our knowledge (information) to perform local work - for example, to implement the quantum demon Maxwell using multilevel systems to cool (purify the state) of qubits in a quantum computer.
As far as quantum engines on a larger scale are concerned, it is too early to argue that such an engine will replace an internal combustion engine. So far, single-atom engines have too low efficiency.
However, it is intuitively clear that when using a macroscopic system with many degrees of freedom, we will be able to extract only a small part of the useful work, because such a system can be controlled only on average. In the concept of quantum motors, it becomes possible to control systems more efficiently.
At the moment, there are many theoretical and engineering issues in the science of nanoscale heat engines. For example, quantum fluctuations are a big problem, which can create "quantum friction", introducing extra entropy and reducing the efficiency of the engine.
Physicists and engineers are now actively working on optimal control of the quantum working fluid and the creation of a nanheater and nanocooler. Sooner or later, quantum physics will help us create a new class of useful devices.
Mikhail Perelstein
