Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems

TL;DR

This paper demonstrates that social inequality measures like Gini and Kolkata indices can effectively predict critical or failure points in various physical system models by analyzing distributions of energy, clusters, or avalanches.

Contribution

It shows how social inequality indices serve as early warning signals for critical transitions in physical models, supported by numerical and analytical results.

Findings

Inequality indices correlate with approaching critical points.

Inequality measures can serve as precursors to system failure.

Numerical and analytical results validate the predictive power.

Abstract

Statistical physicists and social scientists both study extensively some characteristic features of the unequal distributions of energy, cluster or avalanche sizes and of income, wealth etc among the particles (or sites) and population respectively. While physicists concentrate on the self-similar (fractal) structure (and the characteristic exponents) of the largest (percolating) cluster or avalanche, social scientists study the inequality indices like Gini and Kolkata etc given by the non-linearity of the Lorenz function representing the cumulative fraction of the wealth possessed by different fraction of the population. We review here, using results from earlier publications and some new numerical as well as analytical results, how the above-mentioned social inequality indices, when extracted from the unequal distributions of energy (in kinetic exchange models), cluster sizes (in percolation models) or avalanche sizes (in self-organized critical or fiber bundle models) can help in a major way in providing precursor signals for an approaching critical point or imminent failure point. Extensive numerical and some analytical results have been discussed.