Entropy-Topological Method of Analysis of Any Complex Systems with the Participation of Artificial Intelligence

Introduction. Contemporary techno-informational systems are increasingly acquiring the characteristics of complex, multi-level human–machine formations with pronounced cognitive features, in which quasi-cognitive artificial intelligence is employed for information processing, adaptation, and decision-support functions. At the same time, the prevailing information–algorithmic approaches to their analysis fail to account for fundamental properties of the systems under consideration, namely thermodynamic constraints, as well as the role of cognitive and semantic processes that are critical for the stability of such systems. This necessitates the extension of classical entropy-based models and the integration of topological, cognitive, and semantic components into them. The subject of this study comprises methods of thermodynamic analysis based on entropy–topological models and the determination of conditions for their thermodynamic and semantic stability when analysing complex techno-informational systems while taking into account their incommensurable properties. The purpose. The aim of the work is to investigate complex techno-informational systems involving cognitive (human) and quasi-cognitive (artificial intelligence, AI) agencies, considering the incommensurable properties of these systems, by means of thermodynamic analysis using entropy-topological models, and to determine the conditions of their thermodynamic and semantic stability. Results. To achieve this aim, a hierarchical model of system organisation levels-from the physico-energetic to the socio-normative levels - proposed, along with its formalisation in the form of an entropy-weighted hypergraph with multidimensional adjacency matrices. The corresponding scientific novelty lies in the introduction of a set of fundamentally irreducible forms of entropy (physical, informational, cognitive, semantic, socio-normative, etc.), in the formulation of a generalised criterion of thermodynamic-semantic stability of the system, and in the theoretical proof of the impossibility of fully substituting a cognitive agent with artificial intelligence at a certain semantic level. Conclusions. It is demonstrated that AI effectively reduces informational entropy but is not capable of autonomously reducing semantic uncertainty, which establishes fundamental limits to its applicability. The applied relevance of the work consists in the possibility of using the proposed method for the analysis and design of hybrid human-machine systems, for assessing the role of AI in control, learning, and interface solutions, as well as for substantiating human-in-the-loop architectures from the standpoint of thermodynamic and semantic stability.