Analysis of socioeconomic indicators in the United States, Brazil, and other Latin American countries using econophysics techniques

In addressing the complexity inherent in comparing socioeconomic indicators across diverse countries, a substantial barrier arises from the wide array of distinct calculation approaches. Consequently, a highly pertinent question emerges: how does one compare values when the underlying calculation methodologies are diverse? In this context, we propose a multidisciplinary and heterogeneous approach, employing numerical and visual comparisons to analyze socioeconomic indicators of municipalities in the US, Brazil and other Latin American countries. We identify independent-scale patterns in three stages: initially, by compiling a database sourced from respected institutions in each country and identifying correlations within this dataset; next, by creating graphical representations using a binning methodology for scatter plots of the identified patterns; finally, by transforming the dispersions from the initial stage into graphs using a variant of the Gravitational Clustering Algorithm technique from astrophysics. We find significant relationships, specifically in the logarithmic relationship between Municipal HDI and population size. In some countries, global minima were identified, suggesting the existence of a critical population density at which municipalities above this threshold exhibit a positive and significant correlation with an increase in their HDI.