Hi Chris Weston, respectfully I disagree.
With compressed air you have more oxygen molecules in the combustion chamber
More oxygen molecules in the combustion chamber? Only in a turbine. In a piston engine, an 8:1 engine has the same volume of air in the combustion chamber as a 12:1 compression ratio engine. If your theory of more air was important, it would not effect a piston engine (which it does).
and you can burn more fuel per unit time
Burning more fuel per unit time has nothing to do with it. The entire CONCEPT of the original post is about thermodynamic efficiency (ie being able to get more useable work out of the same amount of fuel). Anyone can just increase the fuel flow and get more power out of an engine ... has nothing to do with thermodynamic efficiency.
Let's make it absolutely clear... we are talking about two identical engines, same size, same fuel flow, same RPM, same EVERYTHING - except one has a higher compression ratio - why is the one with higher compression getting more energy out of the same fuel? That's what we are talking about here.