Binary Stochastic Origin, Exponential Law Basis, Long-Range Percolation, and Dissipative Structures — A Unified Physical Framework (UET) for Complex Systems from Underlying Randomness to Strong Emergence

This paper proposes the Unified Emergence Theory (UET), constructing a com-putable and testable physical framework for complex systems from microscopic ran-dom fluctuations to macroscopic strong emergence phenomena. UET takes binarystochastic processes as the microscopic fluctuation basis, deriving the exponentiallaw as the intrinsic statistical form of memoryless stochastic processes; it intro-duces the exponentially saturated dynamic connection probability p(t) to uniformlycharacterize the driving mechanism of material, energy, and information fluxes onsystem critical behaviors; weak emergence is defined as a percolation-type criticalphase transition induced by p(t) → pc under fixed topology (with power-law dis-tribution as its typical statistical fingerprint); strong emergence is strictly definedas a phenomenon that satisfies three physical criteria: (1) number of interactionchannels K ≥ 2; (2) a step change in the number of topological microconfigurations(∆ ln Ωtopo > Ωcrit); (3) the existence of statistically significant downward causa-tion (κ ̸= 0). The theory is strictly based on Prigogine’s entropy change equationfor open systems, establishing a quantitative mapping between stochastic dynamicequations and entropy production rate. UET clarifies that the generation of strongemergence does not depend on the number of primitive types, but on multi-channelcoupling structure, topological plasticity, and cross-level causal closure. The frame-work successfully explains cross-domain phenomena such as bird flocks, snowflakes,neural consciousness, ant colonies, immune systems, financial markets, large lan-guage models, and recommendation systems, and proposes three falsifiable paths.This work provides a quantitative tool with mathematical rigor, physical clarity,and interdisciplinary applicability for the study of emergence in complex systems.