02/16/2017 16:20:52

Quantum systems can violate the second law of thermodynamics, say MIPT’s physicists

The principle of nondecreasing entropy in isolated systems, which is one of the formulations of the much-talked-about second law of thermodynamics, can be violated: It turns out that the entropy of a quantum system can decrease with time. This was discovered by an international team of scientists headed by Dr. Gordey Lesovik, a leading research scientist at MIPT’s Laboratory of Quantum Information Theory and the L. D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences. The research findings were published in Scientific Reports, a Nature Publishing Group journal.

“We found a quantum Maxwell’s demon that can decrease the entropy of a system without even measuring its state,” Lesovik told us.


Maxwell’s demon is a thought experiment created by the physicist James Clerk Maxwell in which he suggested how the Second Law of Thermodynamics might hypothetically be violated.

Most processes in classical physics are independent of time’s arrow. In other words, they can all be run in reverse without breaking any laws. Physicists refer to this property as time symmetry. However, there is one law called the second law of thermodynamics that does not hold under time reversal. As formulated by Rudolf Clausius, this law states that heat can never pass from a colder to a warmer body. This means that heat transfer is a fundamentally irreversible process.

In the 1870s, the principle of increasing entropy was formulated more rigorously by Ludwig Boltzmann in his so-called H-theorem. It describes an isolated system whose state can be described by the kinetic equation which came to be known as the Boltzmann equation. According to this theorem, the entropy of the system can either increase or remain constant. For a long time, the H-theorem could not be proved in the framework of classical statistical physics without resorting to additional constraints. With the advent of quantum mechanics, scientists began to wonder if the H-theorem could be rooted in the quantum world. Eventually, quantum information theory provided important insights into conditions under which the entropy of a system does not diminish.

The team led by Lesovik was the first to formulate the H-theorem using the language of quantum physics. They spent several years trying to prove this quantum analog of Boltzmann’s theorem.

“We began working on it, and it seemed like we were making good progress, but then we found a weak spot. We tried to fix it, but by the time we fixed it, the whole thing started falling apart again. Eventually, we realized that we were onto something. We thought that this theorem might not hold in a quantum system, and maybe that entropy could in fact decrease, even in an isolated system,” said the scientist.

This led the researchers to identify the conditions under which the second law of thermodynamics can be locally circumvented. It can happen in a quantum system of relatively small yet macroscopic size measuring up to several centimeters or even meters. The violation of the second law is possible due to the fact that entropy change manifests itself differently in classical and quantum physics. In a classical system, heat transfer must occur for entropy to decrease. However, as a result of quantum entanglement, the entropy of a quantum system can decrease without any energy being transferred.

“Take Cinderella for example. Her stepmother gives her a bowl of mixed peas and lentils and makes her sort through them, or, physically speaking, reduce the entropy of the system. A classical Cinderella, in an isolated system, would not be able to separate the legumes, whereas her quantum counterpart could. Similarly, we can ‘clean up’ the states of the system by using quantum effects,” Lesovik explained.

He said the team intends to test this effect in the near future by conducting an experiment that will potentially lead to the development of quantum refrigerators and innovative new engines.

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