Traditional social stability research relies heavily on qualitative descriptions and empirical statistics, lacking unified, reproducible, and physically quantifiable theoretical frameworks. To break through the limitations of conventional social science paradigms, this study constructs a pure-energy-dimensional, fully measurable four-layer nested topological entropy model for social systems. Taking human physiological metabolic energy consumption as the microscopic foundation, the model couples neural cognitive energy dissipation, social wealth redistribution, and hierarchical topological friction dissipation, establishing a cross-scale dynamic correlation from individual physiological metabolism to macroscopic social entropy evolution. Adopting the human physiological temperature range of 305 K–310 K as the thermodynamic boundary condition, this study derives the critical Gini coefficient that determines structural instability in social systems. Numerical simulations indicate that social systems with low negative entropy output and high hierarchical internal dissipation yield negative critical Gini coefficients, demonstrating unconditional structural instability. In contrast, steady-state social systems with sufficient negative entropy supply and controllable internal friction present a rigid critical differentiation threshold of 0.15, which is exclusively determined by systemic energy budgets and topological dissipation rather than physiological temperature. Furthermore, by introducing the Belousov-Zhabotinsky (BZ) nonlinear self-organization bifurcation theory, this paper identifies two fundamentally distinct collapse modes in social evolution. Pre-modern agrarian societies with low negative entropy obey subcritical Hopf bifurcation, characterized by sudden and unprompted topological collapse. Modern industrial societies with high negative entropy output follow supercritical Hopf bifurcation, exhibiting gradual, predictable structural degradation. This study verifies that social system collapse is not a single-mode failure but a dual-mode evolutionary behavior governed by energy supply and hierarchical dissipation, providing a quantitative theoretical foundation for social stability assessment and systemic risk prevention.
Xijiang Hu (Fri,) studied this question.