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Cylinder solenoids are indeed a thing

https://en.m.wikipedia.org/wiki/Free-piston_engine

And the Prius uses the Atkinson cycle which is slightly different from the traditional Otto cycle somehow, although I couldn't find a good explanation

https://en.m.wikipedia.org/wiki/Atkinson_cycle

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According to that Wikipedia article, the modern Atkinson cycle trades time spent creating power in the compression phase for time spent extracting energy during the expansion phase, gaining efficiency at the cost of total power.

> creating power in the compression phase

Other than the potential energy of either the heat or the compressed gas, what "power" is created in the compression phase of a normal four stroke ICE?

Pumping losses are greater in a Otto cycle engine due to the increased resistance in compressing the whole stroke. In an Atkinson-cycle you get a longer power stoke than compression stroke and thus are more efficient. There is always another cylinder that get does i take during the short time when valve is open during compression in another cylinder. Thus that cylinder get some free assistance during intake.

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