Axiom System for the Evolution of Nested Dissipative Structures in Human Society Based on Topological Entropy and Time Relaxation Mechanism

Human society is a typical complex giant dissipative system far from equilibrium. Existing dissipative structure theory only macroscopically explains the generation logic of social order, lacking the mathematical definition of hierarchical nested topological structures and the binary distinction between static structures and dynamic temporal evolution, which cannot explain the core paradox of social systems: "unidirectional temporal progression and bidirectional hierarchical rise and fall". Based on fractal topology, non-equilibrium thermodynamics, and BZ oscillation reaction theory, this paper first constructs a static social nested topological entropy model without time parameters, defining a three-level isomorphic dissipative structure of individual-organization-civilization and a five-order cyclic operation chain. Furthermore, three core parameters—time variable, hierarchical time relaxation constant, and system vitality temperature—are introduced to establish a dynamic topological entropy evolution equation set. This paper clarifies that the static nested form of social topological structure is constant, and the time dimension is unidirectionally irreversible, but fluctuations in system energy and negative entropy supply can trigger structural upgrading or degradation. Entropy change disturbances in underlying subsystems are transmitted layer by layer to the parent system, ultimately triggering the critical collapse of the old structure and the self-organized emergence of higher-order dissipative structures. This study constructs a complete theoretical system of static structure ontology, dynamic temporal evolution, and bidirectional hierarchical iteration, providing a rigorous mathematical axiomatic explanation for the rise and fall of human civilization, institutional iteration, and order evolution.