Where do power laws come from?

There exist a handful of famous mechanisms that dynamically lead to scaling laws in complex dynamical systems, including preferential attachment processes and self-organized criticality. One extremely simple and transparent mechanism has so-far been overlooked. We present a mathematical theorem that states that every stochastic process that reduces its number of possible outcomes over time, leads to power laws in the frequency distributions of that so-called sample-space-reducing process (SSR). We show that targeted diffusion on networks is exactly such a SSR process, and we can thus understand the origin of power law visiting distributions that are ubiquitous in nature. We further comment on other examples where SSR processes are able to explain the origin of observed scaling laws.