Scaling the clock frequency
Running for a kilometer takes more energy than walking. In a similar way, maybe running the CPU at a lower frequency can save energy. Let's see.
The power consumption of a CPU when executing code is the sum of a static component, caused by gate leakage current, among other things, and a dynamic component, caused by the switching of the gates:
Pcpu = Pstatic + Pdyn
The dynamic power component is dependent on the total capacitance of the logic gates being switched, the clock frequency, and the square of the voltage:
Pdyn = CfV2
From this, we can see that changing the frequency by itself is not going to save any power because the same number of CPU cycles have to be completed in order to execute a given subroutine. If we reduce the frequency by half, it will take twice as long to complete the calculation, but the total power consumed due to the dynamic power component will be the same. In fact, reducing the frequency may actually increase...
