Comment by yetihehe

It is not a carnot cycle. It will NOT be able to pump heat, it's not a reversible cycle (it's not even a single cycle, it's a series of open-ended heat and pressure transformations). And using a heat-pump will also not make it a perpetual motion. Heat pump can be used as a kind of heat-transformer here, so if you have a lot of low temperature air (but higher than your ambient temp), you could use heat pump to gather energy from that air and present a higher-temperature air for my engine (losing some small amount of heat in the process, but heat pump will reuse heat wasted in it's own electric engine).

It should achieve such efficiency with air heated to 150C and ambient temp of 20C. If you heat air so that it expands more than 2x, it will start to lose efficiency.

BUT - this is all theoretical, I work on simulation that will confirm if it works. It might not, I might have made some big error in thinking how it works, but I searched for 15 years on some way this should not work. I contacted two physics professors specializing in thermodynamics and they couldn't find a way this won't work, both said "Yeah, but to tell more, we need prototype or simulation".