Social entropy: A mathematical framework for measuring disorder in urban welfare distribution systems - Thamrin, Husni; Lubis, Mia Aulina; Sinaga, Randa Putra Kasea; Setiyawan, Andri; Riyaz, Aminath; Remtulla, Asnath Naftali (Al-Jabar: Jurnal Pendidikan Matematika, 2026)
Purpose: This study aims to formulate a multidimensional entropy-based framework for quantifying disorder in urban welfare distribution systems by integrating distributional, institutional, and temporal dimensions within a unified Social Entropy model.Method: The study employed a theoretical and analytical approach grounded in Shannon’s information entropy and complexity science. The proposed framework formulates Distributional Entropy, Institutional Entropy, and Temporal Entropy as complementary components of welfare governance disorder and introduces the Entropy Deviation Index (EDI) to measure divergence between observed welfare allocation patterns and optimal need-based distributions. An empirical illustration involving five major Indonesian cities was conducted to demonstrate the operational applicability of the framework.Findings: The results indicate that welfare distribution disorder is a multidimensional phenomenon arising from the interaction of allocation structures, governance processes, and information dynamics. Composite entropy values ranged from 0.352 to 0.397 nats, indicating moderate levels of systemic disorder across the observed cities. Institutional entropy emerged as the dominant contributor, accounting for 42.3% of total disorder, while sensitivity analysis confirmed the robustness of the framework under alternative weighting specifications.Significance: This study extends the application of entropy theory to welfare governance analysis by introducing Social Entropy as a novel quantitative framework for measuring multidimensional disorder. The proposed model provides policymakers and researchers with an integrated tool for diagnosing welfare distribution inefficiencies, evaluating governance performance, and supporting evidence-based decision-making in complex urban environments.