# Approaching the Carnot Limit at Finite Power: An Exact Solution

The Carnot heat engine sets an upper bound on the efficiency of a heat engine. As an ideal, reversible engine, a single cycle must be performed in infinite time, and so the Carnot engine has zero power. However, there is nothing in principle forbidding the existence of a heat engine whose efficiency approaches that of Carnot while maintaining finite power. Such an engine must have very special properties, some of which have been discussed in the literature, in various limits. Here, an exactly solvable model is presented for the first time. The equations of state have their origins in the extended semi-classical thermodynamics of electrically charged black holes.

**Comments:**4 pages, 2 figures

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