As a side note, engineers have designed ways of capturing lost exhaust energy for quite some time. Turbochargers are one example, but more specificially, using turbo-compounding.
Turbo-compound engine - Wikipedia, the free encyclopedia
It is true that when the piston is nearing BTC and the exhaust valves open, there is still a lot of pressure left over in the cylinder. It is released into the exhaust manifold and basically wasted, because it has simply "run out of time" to produce effective energy. Turbo-compounding was used in WW2, where exhaust gasses would spin a turbine, much like in a turbocharger, but this energy was used to physically help turn the crankshaft, unlike a turbocharger. Currently, the DD15, a heavy duty truck engine, also employs such a design. This engine has a VGT turbo for supplying boost pressure, and also a compound turbo that physically drives the gear train at the back of the engine to supply an extra 50 "free" horsepower. Interesting.
My idea combines the disabling half the cylinders with compound-turbocharging. As an example, I will use my motorcycle, a 400cc four stroke parallel twin.
One cylinder will run normally. It will be called the "power cylinder." The other cylinder will be turned into the "compound cylinder." With some fancy welding and machining, we will add two bumps 180 degrees away from the normal intake and exhaust bumps on the cam lobes, so the valves open twice during one camshaft rotation, turning it into a 2-stroke "air compressor" of sorts, giving it twice the capacity of the power cylinder. The exhaust from the power cylinder is routed through an increased diameter "accumulator", necessary because of mismatched timing between the two cylinders, and then into the intake port of the compound cylinder. The exhaust port of the compound cylinder exhausts to the normal exhaust system.
How it works. Exhaust from the power cylinder, builds pressure in the pipe between the power cylinder exhaust port and compound cylinder intake port. When the air/fuel in the power cylinder is ignited, it expands to maybe five times its volume. The double capacity compound cylinder takes advantage of a higher volume, lower pressure exiting the power cylinder and turns it into energy to drive the crankshaft.
A four cylinder car could be turned into a 2/2 power/compound cylinder engine. Or a V6 into a 3/3. Would it work? Probably. Well? Who knows. I can see compound piston cooling being a big issue, since there would be no cool intake charge to moderate temps. Most importantly: what would we call it? A catchy name is mandatory. Maybe THIS is the question I need to ask!