Entropy–Topological Analysis of Selected Classes of Complex Multicomponent Systems

This paper proposes an entropy–topological method for the analysis of multicomponent complex systems that accounts for the relative incompatibility of system parameters, in particular physical, chemical, and other mechanisms, with configurational, thermodynamic, and other system properties. The relevance of the study is determined by the insufficient formalization of existing approaches to the description of multicomponent complex systems and the need for a universal quantitative criterion characterizing their structural and functional organization. The scientific novelty of the proposed approach lies in the decomposition of the total entropy into a spectrum of interrelated constituents and in representing the system as a multilayer network structure augmented by its thermodynamic parameters. This representation makes it possible to investigate a wide range of mutually incommensurable properties of a complex system, including its structure, information content, functionality, physicochemical features, surface phenomena (including interfaces with a supersystem), the capacity for thermodynamic imbalance, and kinetic behavior, depending on the intrinsic nature of the system under consideration. The practical applicability of the method is demonstrated through an analysis of the functional properties of geopolymer materials produced from metallurgical waste, for which an aggregated quality index is introduced that links entropy-based parameters with operational performance characteristics. The obtained results extend the capabilities of thermodynamic and information-theoretic modeling of certain classes of complex systems.