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Traditionally, internal combustion engines follow thermodynamic cycles comprising a fixed number of crank revolutions, in order to accommodate compression of the incoming air as well as expansion of the combustion products. With the advent of computer-controlled valve trains, we now have the possibility of detaching compression from expansion events, thus achieving an “adaptive cycle” molded to the performance required of the engine at any given time. The adaptive cycle engine differs from split-cycle engines in that all phases of the cycle take place within the same cylinder, so that in an extreme case the gas contained in all cylinders can be undergoing expansion events, resulting in a large increase in power density over the conventional four-stroke and two-stroke cycles. Key to the adaptive cycle is the addition of a variable-timing “transfer” valve to each cylinder, plus a space for air storage between compression and expansion events.