why power is lower if memory accesses are spread over a longer time?

Question

I am studying Intel speed shift, I saw a sentence:

"If these memory accesses are spread over a longer time, the power is lower but the energy is equal"

My understanding is that when longer runtime, we need more energy even platform power is constant.

I think power = V x I at a testing moment.

Why power became lower if memory accesses are spread over a longer time ?

ref: http://webee.technion.ac.il/~ran/papers/IEEE-Computer-H-EARtH-2016.pdf

page.35,

"Fixed energy (not shown in Figure 2): During workload execution, a fixed amount of data is transferred to and from memory, disk drives, and so on. This activity is a function of the application footprint and the devices’ physical characteristics; it does not depend on CPU frequency and therefore translates to fixed energy. If these memory accesses are spread over a longer time, the power is lower but the energy is equal"

Answer 1

"My understanding is that when longer runtime, we need more energy even platform power is constant."

This is mistaken.

Apart from minor leakage, energy consumption in modern computational circuits is spent almost exclusively changing state, not "just sitting there". In engineering terms we say that the dominate consumption is dynamic not static - and it is basically the cost of charging or discharging the parasitic capacitances by sending currents through paths where some is lost as heat.

So if you have the same number of state changes to make, spreading that amount of a greater period of time would mean a lower average power than doing it in a shorter period of time. The analysis you are reading is looking only at the cost of a particular type of I/O.

The processor may be doing other things during those times, which would consume energy. If it were a very outdated design it might even keep running at a high clock rate and busy waiting for something useful to do. But modern designs don't do that - if there is nothing useful to do, the clock drops, and in the more efficient designs (like phones that run on battery) the clock to all but some essential housekeeping eventually stops when there is nothing useful to do.