2025/05/21 by Marco Menale, Giuseppe Toscani, Menale, Marco +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #35Q20 35Q84 91B80 #Advanced Thermodynamics and Statistical Mechanics #FOS: Economics and business #FOS: Physical sciences #General Finance (q-fin.GN) #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.2505.15526
openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors. The macroscopic dynamics of their mean values follow a Lotka-Volterra system of ordinary differential equations. Unlike classical models of wealth and opinion formation, which tend to converge toward a steady-state profile, the oscillatory behavior of these densities only leads to the formation of local equilibria within the Fokker-Planck system. This makes tracking the evolution of most inequality measures challenging. However, an insightful perspective on the problem is obtained by using the coefficient of variation, a simple inequality measure closely linked to the Gini index. Numerical experiments confirm that, despite the system's oscillatory nature, inequality initially tends to decrease.