The Physical Roots of Complexity:. Renewal or Modulation?

We show that the emergence of a non-Poisson distribution might have different physical origins. We study two distinct ways to generate a non-Poisson distribution, the first from within the renewal theory, and the second based on infinitely slow modulation, a condition that makes this second perspective equivalent to superstatistics. We prove that these different origins yield different physical effects, aging in the former case, and no aging in the latter.