Exponent Spectrum of Lorenz Curves and Its Relation to a System's Heterogeneity

We analyze the effect of microscopic heterogeneity on the Lorenz curve of macroscopic observables. The Lorenz curve of a response function, being a cumulative and bounded quantity; it is often a more stable function than the corresponding probability density. We show here that by doing an exponent spectrum analysis of the complementary Lorenz curve, it is possible to obtain a reflection of the underlying heterogeneity that causes the response function to depart from a power law behavior. We demonstrate this framework first by synthetic data and then by analyzing the avalanche statistics of a two dimensional, Random Field Ising Model (RFIM) at zero temperature. This method can lead to possible use in estimating the microscopic heterogeneity of a system from the analysis of an estimated Lorenz curve, particularly in socio-economic and physical contexts where the full probability distribution function is unavailable.