A METHOD FOR ANALYZING MULTICOMPONENT COMPLEX SYSTEMS BASED ON MULTIDIMENSIONAL MATRICES OF ADJACENCY AND ENTROPY RELATIONS BETWEEN SYSTEM COMPONENTS
DOI:
https://doi.org/10.20535/kpisn.2026.1.350050Keywords:
complex system, multicomponent nature, entropy, adjacency matrix, multilayer structure, entropy structuring.Abstract
Background. Existing methods for analysing multicomponent complex systems account only weakly for the relative incompatibility of system parameters, in particular the interplay between physical, chemical, and other mechanisms and the configurational, thermodynamic, and additional properties of the system. The challenge of achieving a stable, practically formalised investigation of the development of complex systems—through a mathematically simplified and conceptually transparent set of indicators enabling comprehensive analysis—remains unresolved.
Objective. The development of an alternative method for maximally comprehensive and simplified analysis of multicomponent complex systems, based on their functionality, structural organisation, and inherent properties.
Methods. A method for analysing complex systems by means of multidimensional entropy-structured adjacency matrices is proposed as a derivative model for describing their multicomponent nature. Entropy and its variation, which reflects changes in the state of the system itself, are proposed as thermodynamic indicators of multicomponent systems.
Results. The first essential feature of the model lies in the partitioning of the total entropy of the entire system into superpositional components corresponding to the parameters of the system’s properties, which forms the basis for a certain universality of the method. The second significant distinction of the model is associated with its multilayered nature within the adjacency matrix. This enables the investigation of a wide spectrum of incomparable properties of a complex system, including its structural organisation, informational characteristics, functionality, physico-chemical features, surface phenomena—including the boundary with the supersystem—as well as its capacity for thermodynamic nonequilibrium and kinetic behaviour, depending on the nature of the system itself. The validation and advantages of the model are demonstrated through several practical examples from the field of metallurgical waste recycling, where mixtures are considered as multicomponent systems used in the production of metallurgical briquettes as secondary raw materials for this industrial sector.
Conclusion. A qualitatively new approach has been developed for the study of multicomponent complex systems by means of a multidimensional entropy-containing adjacency matrix, which describes interrelations through the total entropy decomposed into individual components. Its relative universality and practical applicability are demonstrated.
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