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The invariance property of the mean path length is an astonishing law ofNature governing the motion of particles inside a disordered material. Whateverthe strength of the disorder, the property states that the mean path length isexclusively determined by the ratio between the volume and the surface. Tillnow, the property has been reported as universal and valid in any kind ofdisordered medium and also beyond diffusion conditions. Nevertheless, we foundout that the property fails in anomalous transport and in other kinds of randomwalk. By means of Monte Carlo simulations of light transport, we show that, inthese cases, the invariance property loses its validity and the mean pathlength becomes dependent on the diffusive characteristics of the medium. Thecritical issue of such a violation lies in the breaking of isotropy andhomogeneity of the radiance in the whole volume. These results are valid forall natural or artificial phenomena where random walkers, whatever theirnature, are able to experiment anomalous transport.

Violation of the mean path length invariance property