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This study investigates the sustainability, resilience, and institutional performance of urban governance systems by operationalizing key thermodynamic principles energy, exergy, entropy, equilibrium, open systems, and irreversibility within a political and behavioral systems framework. Urban political systems are conceptualized as open, non-equilibrium systems, characterized by continuous flows of resources, information, and institutional feedback across metropolitan governance structures. Within this model, energy represents systemic inputs to urban governance, exergy denotes usable governing capacity at the city and metropolitan scale, and entropy reflects levels of institutional disorder, inefficiency, and systemic degradation affecting urban sustainability. The study first formulates a conceptual analytical model defining urban political entropy and systemic exergy as measurable variables associated with institutional stability, crisis-management capability, adaptability, and reform potential in urban and metropolitan governance. It then conducts a comparative empirical analysis of Germany, Türkiye, China, and South Africa using normalized indicators derived from international datasets for 2023, with particular attention to their implications for urban governance capacity and city-level institutional performance. These indicators are employed to construct proxy measures for the Exergy Efficiency Ratio, Societal and Institutional Entropy, and overall urban governance capacity. The comparative results reveal that open and decentralized governance systems tend to maintain higher exergy efficiency and lower entropy levels at the urban scale, whereas highly centralized systems, although effective in resource mobilization, tend to accumulate greater systemic entropy over time. Transitional governance systems exhibit hybrid and fluctuating thermodynamic characteristics in their urban institutional structures. The findings empirically support the Thermodynamic Model of Political Systems and demonstrate its utility as a predictive and diagnostic framework for evaluating urban institutional efficiency, resilience, and sustainability. By quantifying political energy flows and entropy dynamics within urban governance systems, this study contributes to the development of an integrated systems thermodynamics of cities and provides a robust analytical foundation for sustainable urban governance, institutional reform, and long-term strategic policy design.