Hi Blackhand.
Are you sure about this?
Look, I'm sure we all know that a piston engine with the same physicals can't have a different compression ratio, and in order to change it without changing the shape of the cylinder you would end up changing the volumetric capacity very slightly.
So, for the purposes of answering the original post, yes, if the capacity of the engines is the same, the compression ratio will not change the amount of air molecules. Lets say 2x 350 cubic inch engines - you will theoretically have the same amount of air in the cylinder at TOPD if it has a 8:1 or 15:1 compression ratio.
From work on performance engines, it is the compression pressures and not really the comp ratio that is important. Compression pressures are related to the comp ratio but are more influenced by valve and ignition timing. Of course the dynamics of the intake and combustion chambers has a direct affect.
I've talked about this before, and the fact that it relates to limitations of how a piston engine is operated (ie at inefficient high RPM or across a wide RPM band, low throttle settings etc). Not related to the OP, which was about how compression, and compression alone makes a difference in thermodynamic efficiency.
I work on the practical side, so is interesting talking to a theorist - unless of course you are just a sciolist.
Nope, no sciolist. Just someone with a basic knowledge of physics. As an engine tuner, I'm sure you know more about me on how to tune an engine on a dyno for best power and driveability over a large RPM range... interesting, but not related to the OP, nor the thermodynamic efficiency of an engine. It really is simple physics.