Why system energy is equal to 1/f?
Power Management



That diagram is in the section of the slidedeck where they're talking about power management is stating that the energy efficiency for System's on a Chip (SoC) will behave inversely proportional to the frequency of the CPU as it increases. Power spectral density is inversely proportional to the frequency of the signal.

This diagram might help illustrate this effect a bit more:



Imagine that as the CPU's over frequency increases, or as frequencies of the RAM or various busses increase, the amount of power available to leverage will be in a relationship that will be most like the graphic showing the frequency domain (lower right).


NOTE1: the relationship of 1/f is very common in nature and is typically called fractal noise" or "pink noise".
NOTE2: This is also why Fourier transforms are important in our field.


Additional details

The main author of the slidedeck you reference, Efraim Rotem, also wrote this paper titled: H-EARtH: Heterogeneous Multicore Platform Energy Management.

In this paper he mentions this:


  Platform components consume fixed runtime power with energy
  proportional to runtime (1/f). All other components are ignored. The
  two opposite energy trends might have a global minimum (see Figure 1).


References

These are helpful in understanding many of the concepts that are key to grasping all this.


1/f like noise and self organized criticality
Pink noise
Colors of noise
Chapter 6 - ENERGY MANAGEMENT TECHNIQUES FOR SOC DESIGN
Learn how to create "pink" noise
But what is the Fourier Transform? A visual introduction