  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.
