I posted this question at Math Stack Exchange a few weeks ago without any luck. It occurred to me I might have more luck by posting it here. The basic question is whether there exists a known relationship between the period of a signal (i.e. the inverse of the frequency) and its corresponding power, such as that depicted in the graph in the linked post.
There is no universal relationship between power and period length. These are two unrelated, yet completely independent, concepts (see amplitude vs. frequency).
But what your plot might be referring to is a digital CMOS circuit. Such a circuit consumes a certain amount of energy per clock cycle. Hence for this kind of device, power consumption is (approximately) proportional to clock frequency.
So it depends on the origin of the data. There is no universal relation, but there might be one for specific situations.