This article explores the question of whether concepts and methods used in non-equilibrium statistical physics, already successfully applied in biology, epidemiology and finances, can also be a useful tool for research into economic development. The aim of this article is to describe one such phenomenon, the phenomenon of “fat tails”, for a multi-disciplinary public and to stimulate discussion on its potential use. The method is explained and empirically tested by looking at the example of the probability distribution of per capita GNP in various countries. It is shown that this distribution does indeed have “fat tails”. The significance of the appearance of such fat tails is discussed and it is stressed that they reflect a complex dynamic which cannot be captured using only mean values and variances. The article also suggests some other pertinent problems of development research where they may possibly be applied.