I am trying to pick up what you're putting down, Nutcase, and I have some questions. I thought the richer mixture was to add a safety buffer for the cylinders and to prevent cats from overheating, not to reduce NOx emissions. I think lacing fuels with ethanol, raising operating temps, adding compression, and variable valve timing, etc do more to reduce emissions than running a richer tune.
As for the Otto cycles being inefficient, are you implying Atkinson engines are better? The latter is more at home in hybrids I thought, not performance cars.
when there is more fuel available there is more carbon available. CO2 is has a lower energy level (more stable than) NOx. So when there is more carbon available the reaction trends to CO2 over NOx. Parts of oxygen vs parts of nitrogen in the air always stay the same. So by consuming more oxygen to make CO2 you reduce the amount of NOx that can be made.
by burning access hydrocarbons you also make available more hydrogen to bond with oxygen and form water which is also very stable and low energy.
this is the same idea of how ethanol works to help emissions. even though every ethanol molecule carries oxygen the balances are different.
but as you may know you can make more power and improve MPG by leaning out this mix. This is how tuners get 30 more hp and increase MPG on a stock mustang just through a tune.
atkinson being more efficient that otto has a huge "it depends" attached. regular otto cycle engine of the same displacement can be made physically smaller. atkinson cycles also have a narrow rpm range and because hot air/fuel gets pushed back into the intake manifold before modern computer controls the intake mani was literally a bomb.
when I said the otto cycle was inefficient I was referring to how efficiently it can turn potential energy into mechanical energy. The best otto cycles in a laboratory environment are only 36% thermally efficient. but inefficient does not automatically mean ineffective. liquid fuel is easy to store and transfer, the engine is internal combustion as opposed to a rocket or something, nor is it a nuclear reactor, and it produces rotational energy which is easy to translate into our wheels turning.