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Mathematics proves cooling to absolute zero impossible

Mathematics proves cooling to absolute zero impossible

The University College London has mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law of thermodynamics.

In 1906, German chemist Walther Nernst formulated the heat theorem, which states that as a perfect crystal approaches the absolute zero point of 0 kelvin (-273.15°C), the system’s entropy also goes to zero. This work earned him the 1920 Nobel prize in chemistry.

The rule was controversial, with heavyweights like Albert Einstein and Max Planck debating it and introducing their own formulations. In 1912, Nernst defended his version by adding another clause, the unattainability principle, which states that absolute zero is physically unreachable.

Taken together, these two rules make up the modern third law of thermodynamics.

But because earlier arguments focused only on specific mechanisms or were crippled by questionable assumptions, some physicists have always remained unconvinced of its validity.

Mathematical proof
Now Jonathan Oppenheim and Lluís Masanes at University College London have mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law.

“In computer science, people ask this question all the time: how long does it take to perform a computation?” says Oppenheim. “Just as a computing machine performs a computation, a cooling machine cools a system.” So, he and Masanes asked how long it takes to get cold.

Cooling can be thought of as a series of steps: heat is removed from the system and dumped into the surrounding environment again and again, and each time the system gets colder. How cold depends on how much work can be done to remove the heat and the size of the reservoir for dumping it.

By applying mathematical techniques from quantum information theory, they proved that no real system will ever reach 0 kelvin: it would take an infinite number of steps.

Getting close to absolute zero is possible, though, and Masanes and Oppenheim quantified the steps of cooling, setting speed limits for how cold a given system can get in finite time.

Removing uncertainty
As quantum computing advances, the need to quantify cooling becomes more pressing. To store data, the particles in a quantum computer are put in particular energy states; extra energy and the warmth that it brings push particles out of those states, degrading or destroying the stored data.

“It’s not just removing the energy of the system,” Masanes says. “It’s also about removing uncertainty.”

The limits set by this research are far less stringent than the technological limitations for now: nobody has reached temperatures or cooling speeds near what Masanes and Oppenheim found are the bounds. As technology improves, they hope that these bounds will start to become practically relevant.

“The work is important – the third law is one of the fundamental issues of contemporary physics,” says Ronnie Kosloff at the Hebrew University of Jerusalem. “It relates thermodynamics, quantum mechanics, information theory – it’s a meeting point of many things.”

Journal reference: Nature Communications, DOI: 10.1038/ncomms14538

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