Intelligence vs Entropy: Mathematical Modelling within the Framework of the Theory of Intelligent Evolution and Hamzah Equation.

Orcid ID: https://orcid.org/my-orcid?orcid=0009-0009-3175-8563 Science Open ID: https://www.scienceopen.com/user/2c98a8bc-b8bb-49b3-9c91-2f2986a7e16e Safe Creative register the work titled "The Theory of Intelligent Evolution, the Hamzah Equation, and the Quantum Civilisation". Safe Creative registration #2504151474836. ......................................................................................................................... This study examines the fundamental relationship between two pivotal concepts — entropy (as a measure of disorder and uncertainty) and intelligence (as the capacity to diminish disorder and create order) — within the framework of the Theory of Intelligent Evolution. The work begins by providing precise definitions of entropy as applied in physics, mathematics, information theory, and computer science, before expounding the concept of intelligence across individual, societal, cosmic, and computational dimensions. Through the application of mathematical modelling, machine learning algorithms, complexity theory, and optimisation equations, the research simulates the dynamic interplay between these two forces. The findings indicate that entropy does not merely generate challenge and disorder, but rather serves as the principal driver for the growth of intelligence and the adaptive capacity of systems. Conversely, intelligence functions to reduce entropy, thereby enabling higher levels of coordination, predictability, and efficiency. This reciprocal interaction, observable across domains such as quantum physics, biology, social sciences, and emerging technologies, plays a decisive role in the formation and stability of complex structures. In essence, the study demonstrates that the evolution of intelligence is inextricably linked to its capacity to respond to — and indeed be stimulated by — the very presence of entropy, shaping not only the trajectory of human and cosmic development but also the architecture of artificial systems.