Algebraic–Informational Formalization of Niklas Luhmann's Social Systems Theory

This work proposes a formal translation of the central concepts of Niklas Luhmann’s social systems theory into an algebraic–informational framework. The article establishes structural correspondences between key sociological notions — communication, autopoiesis, observation, functional differentiation, and binary coding — and mathematical constructions derived from operator algebras and information theory. Communication is modeled as morphisms between algebras of observables, autopoiesis as algebraic closure under endomorphisms, observation as the selection of subalgebras through partial trace operations, and functional differentiation as algebraic decomposition into subsystems operating under distinct binary codes. The goal of the formalization is not to replace Luhmann’s conceptual theory but to provide a mathematical language capable of clarifying structural relations, reducing conceptual ambiguity, and enabling the definition of measurable quantities such as communicational entropy, structural coupling, and systemic stability. The proposed framework opens a research program at the interface between systems sociology, mathematical modeling, and information theory, suggesting new analytical tools for the study of complex social systems while preserving the interpretative depth of Luhmann’s original theory.