Abstract
Monte Carlo (MC) simulations are the gold standard for describing various transport phenomena and have largely contributed to the understanding of these processes. However, while their implementation for classical transport governed by exponential step-length distributions is well-established, widely accepted approaches are still lacking for the more general class of anomalous transport phenomena. In this work, a set of rules for performing MC simulations in anomalous diffusion media is identified, which is also applicable in the case of finite-size geometries and/or heterogeneous inclusions. The results are presented in the context of radiative transfer, however their implications extend to all types of anomalous transport. The proposed set of rules exhibits full compatibility with the pathlength invariance property for random trajectories, and with the important radiometric concept of fluence. Additionally, it reveals the counter-intuitive possibility of introducing interfaces between independent subdomains with identical properties, which arise from the fact that non-exponential step-length distributions have a "memory" that can in principle be reset when traversing a boundary. These results have far-reaching consequences not just for the physical interpretation of the corrections required to handle these discontinuities, but also for their experimental verification, due to their expected effects on the observable pathlength distributions.