Yes. Most of the power goes into charging and discharging the capacitance inherent in each wire and transistor gate every time a signal changes. When you shrink

Yes. Most of the power goes into charging and discharging the capacitance inherent in each wire and transistor gate every time a signal changes. When you shrink by 2x, the capacitance goes down by about 4x (because it's proportional to area) and power goes down 4x also. (It's not exactly square-law, because the sides of wires have capacitance too, but at least at larger sizes it was close.) See https://en.wikipedia.org/wiki/Dennard_scaling https://en.wikipedia.org/wiki/Dennard_scaling for details.