(Anti)Gravitron: A Statistical Physics Perspective on Multidimensional Metrics of Polarizing Inequality

(Anti)Gravitron: A Statistical Physics Perspective on Multidimensional Metrics of Polarizing Inequality | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article (Anti)Gravitron: A Statistical Physics Perspective on Multidimensional Metrics of Polarizing Inequality Rolando Manuel Gonzales Martinez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7900636/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper introduces a novel framework for measuring multidimensional inequality based on a statistical physics reinterpretation of centrifugal and centripetal forces in rotating systems. Inspired by the mechanics of the Gravitron and extended via the conceptual AntiGravitron---a thought experiment that models the polarization dynamics of social inclusion and exclusion---this study proposes a new class of inequality metrics grounded in multivariate mixtures of Beta distributions. These composite metrics capture three key structural dimensions of polarizing inequality: the number and balance of population clusters (modal entropy), the internal uniformity of each cluster (concentration), and the separation between clusters in attribute space (geometric divergence). Building on analogies from magnetohydrodynamics, non-equilibrium statistical mechanics, and entropy-based modeling, the AntiGravitron conceptualizes inequality not as a scalar deviation from equality, but as an emergent property of multimodal distributional geometry in bounded domains. Monte Carlo simulations of the AntiGravitron show how bifurcation, stratification, and polarization jointly influence inequality measurements due to multidimensional attraction-repulsion forces. An empirical application of the AntiGravitron to US household income data reveals polarized inequality driven by intersecting centripetal and centrifugal socio-economic forces affecting Black and African American populations in the Philadelphia County. By bridging physical systems theory and social stratification analysis, this paper offers a rigorous, flexible, and interpretable metric that enhances the understanding of polarizing inequality in high-dimensional, structurally heterogeneous contexts. The AntiGravitron framework holds promise for small-area estimation of polarization-driven inequality in socio-economics and biomedicine domains such as epidemiology, where inequality arises from multi-axial exclusion and attractor dynamics. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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Inspired by the mechanics of the Gravitron and extended via the conceptual AntiGravitron---a thought experiment that models the polarization dynamics of social inclusion and exclusion---this study proposes a new class of inequality metrics grounded in multivariate mixtures of Beta distributions. These composite metrics capture three key structural dimensions of polarizing inequality: the number and balance of population clusters (modal entropy), the internal uniformity of each cluster (concentration), and the separation between clusters in attribute space (geometric divergence). Building on analogies from magnetohydrodynamics, non-equilibrium statistical mechanics, and entropy-based modeling, the AntiGravitron conceptualizes inequality not as a scalar deviation from equality, but as an emergent property of multimodal distributional geometry in bounded domains. Monte Carlo simulations of the AntiGravitron show how bifurcation, stratification, and polarization jointly influence inequality measurements due to multidimensional attraction-repulsion forces. An empirical application of the AntiGravitron to US household income data reveals polarized inequality driven by intersecting centripetal and centrifugal socio-economic forces affecting Black and African American populations in the Philadelphia County. By bridging physical systems theory and social stratification analysis, this paper offers a rigorous, flexible, and interpretable metric that enhances the understanding of polarizing inequality in high-dimensional, structurally heterogeneous contexts. 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