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energy is work, and cpus do no work. from a purely electrical standpoint, they are resistive heaters. some energy goes into switching the state of transistors, but that state change generates heat.
basically, if you flip a power switch, the energy doesn't go into the state of the switch (which is information), but the act of flipping it.
yea, they do work on the flow of electrons. switching the channels of electron flow is work.