[arbitrandomuser]

carnot theorem does not put an absolute limit , a carnot cycle can have any efficiency as long as you have reservoirs hot and cold enough ,

besides that if you could be more efficient than carnots cycle at two temperature you can spontaneously extract heat from a cold object and out it in a hot object without any input energy , this would mean you can have perpetual motion . we are not just going to bump a kardashev scale , were going to truly max out and go beyond.

fun fact the U S patent office has been bogged down by so many perpetual motion applications they have made it policy to outright reject such applications without a working model satisfactorily demonstrating it

[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".