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Anytime engineers try to design a new kind of heat-based engine or improve on an existing design, they bump up against a fundamental efficiency limit: the Carnot Limit.

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"The formula for the Carnot limit is

max efficiency of a heat engine = 1 - Tcold/Thot  

i.e. complete reversibility

Classically both absolute temperatures are positive and obviously Tcold < Thot, therefore the efficiency is less than 1.

However in quantum theory we can have negative temperature from quantization of energy. Indeed, a coherent laser beam is an example (population inversion is an effective negative temperature in an open pumped system). Any negative temperature has more energy than any positive temperature for the same system. So what happens is Tcold is positive, but Thot is negative? The efficiency is greater than 1 i.e. "over-unity" - the Holy Grail." Jack Sarfatti

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