Convergence of Needs-Dependency Social System Evolution

Abstract: How the ordered structure of a social system emerges from the interactions of individual needs is a core
question in sociological theory. This paper traces the foundation of Needs Dependency Theory (NDT) back to the
thermodynamic necessity of living systems counteracting entropy, defining "need" as a signal or request for
negative entropy by a subject, "dependency" as the projection of need between subjects, and "dependency
relations" as the basic structural units of a social system. On this basis, the paper introduces the simulated
annealing algorithm as a mathematical model for the evolution of social systems, proving that under certain
conditions, the system inevitably converges to a globally optimal dependency structure. Furthermore, through themonotonic decrease theorem of dependency entropy, it reveals the spontaneous growth mechanism of social order.
The paper further distinguishes the ontological differences between physical annealing (exogenous temperature,
passive atoms) and the annealing of living systems (endogenous temperature, active comparison), pointing out that
the "heating up" of a social system originates from interactions between subjects and their environment but is
primarily driven by an internal loop of perception, comparison, need generation, and dependency reconstruction,
rather than by external operator commands. Mill's theory of reciprocal demand and resource dependency theory
serve as historical footnotes for NDT in specific contexts, rather than its theoretical origins. This work provides a
unified path grounded in thermodynamics for the formalization and computability of sociological theory