I never said it's not as efficient, I just said it's not as good as you make it out to be. I think in the last several posts I explained that yes it does improve efficiency. But it cannot utilize pure thermal energy. I'll let someone else try to explain, I think I've done the best I can.
I'll try to clarify one more thing. A turbocharger is barely more efficient than a supercharger. Both are deprovements over a naturally aspirated engine running full power, Otto cycle with blowby losses. The best thing about a turbocharger is that the design lends itself to very high specific power achievable.
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