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The concept of a perpetual motion machine is an enticing one: Imagine a machine that runs continuously without requiring any external energy—a feat that could make refueling vehicles a thing of the past.

While a perpetual motion machine inspires appealing possibilities, most scientists agree that such a machine is impossible, as the very concept—doing work without any energy input—defies the laws of thermodynamics. Nevertheless, some researchers have forged ahead with efforts to create systems resembling perpetual motion at microscopic scales, including spin systems and ultracold quantum gas, which have suggested that perpetual motion machines may be more than pie-in-the-sky notions.

But now, mathematicians at MIT and the Max Planck Institute for Astrophysics have challenged these ideas with equations showing that such systems, while innovative, do not illustrate the dynamics of perpetual motion. The main claim of such experiments is that they are able to produce systems with negative absolute temperatures, or temperatures below 0 degrees Kelvin. If true, such systems could be used to build machines that produce more work than the heat energy put into them—a key characteristic of perpetual motion.

In a paper published this month in the journal Nature Physics, the researchers analyzed past claims of negative absolute temperature and found that in all cases, scientists were interpreting experiments based on a flawed—though universally accepted—definition of entropy, or heat. This definition, called the Boltzmann entropy, appears in modern physics textbooks, and is widely used to calculate the absolute temperature of a wide range of physical systems.

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