Investigating inequality: a Langevin approach

Inequality indices are quantitative scores that gauge the divergence of wealth distributions in human societies from the "ground state" of pure communism. While inequality indices were devised for socioeconomic applications, they are effectively applicable in the context of general non-negative size distributions such as count, length, area, volume, mass, energy, and duration. Inequality indices are commonly based on the notion of Lorenz curves, which implicitly assume the existence of finite means. Consequently, Lorenz-based inequality indices are excluded from the realm of infinite-mean size distributions. In this paper we present an inequality index that is based on an altogether alternative Langevin approach. The Langevin-based inequality index is introduced, explored, and applied to a wide range of non-negative size distributions with both finite and infinite means.