Heterogeneity explains features of "anomalous" thermodynamics and statistics.

Abstract

Phenomena characterized by power-law probability distributions abound in nature and the applied sciences. We show that many of these power laws are well described by the Student, or t, distribution, and we discuss the origin of this universality based on three examples (Brownian motion, Knudsen diffusion in rough pores, and bubbly multiphase flow). These case studies are representative for a large class of systems with heterogeneous features, examples of which can be found from Earth sciences to astrophysics, and even in the social sciences. We show that common forms of polydispersity, such as polydispersity arising naturally as a result of aggregation-fragmentation phenomena, typically lie at the basis of the observed scaling. We conclude that complicated arguments based on long-range correlations or nonergodicity are often incorrect or misleading in explaining many naturally observed power laws and, in particular, those described by the Student distribution.