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Physicists are developing new experimental tools to build engines, refrigerators, and other thermodynamic machines with quantum components. Such machines are not only small, but they might also possess unexpected capabilities compared to their classical counterparts. Finding the fundamental limits on how these machines operate—a set of thermodynamic laws that apply on the quantum scale—is therefore an important theoretical goal. In independent papers, Piotr Ćwikliński from the University of Gdansk, Poland [1], and colleagues, and Matteo Lostaglio at Imperial College, UK, and colleagues [2] have derived a set of such laws, akin to the second law, for quantum systems that exist in a coherent superposition of states. These laws spell out the restrictions for how such a system can evolve under any physically plausible operation, thus providing ultimate limitations that even quantum machines cannot overcome.

Theoretical thermodynamics has always been practically motivated. Its aim is to develop principles that tell us what types of machines we can build, and the limits on their efficiency and output. Our ability to manipulate a system depends on the information we have about its state. Recent efforts to understand the thermodynamics of quantum systems have therefore been inspired by quantum information theory [3], a field perhaps best known in connection with quantum cryptography and computing.

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