Article 4420

Title of the article



Ostreykovsky Vladislav Alekseevich, doctor of technical sciences, professor, sub-department of computer science, Surgut State University (1 Lenin street, Surgut, Russia), E-mail:
Lysenkova Svetlana Aleksandrovna, candidate of physical and mathematical sciences, associate professor, sub-department of computer science, Surgut State University (1 Lenin street, Surgut, Russia), E-mail:
Shevchenko Elena Nikolaevna, candidate of physical and mathematical sciences, associate professor, sub-department of computer science, Surgut State University (1 Lenin street, Surgut, Russia), E-mail: 

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Background. It is possible that one of the important reasons for a large number of accidents and disasters is the incomplete consideration of their living conditions when designing structurally and functionally complex systems (SSSS), including shortcomings in the calculation of durability, taking into account the instability and irreversibility of processes in the equipment of
dynamic systems. At the same time, special attention is paid to the issues of simultaneous consideration of the existence of various factors of a constructive and operational nature in the conditions of time asymmetry in the pastpresent-future modes. Without knowledge of the influence of a complex of environmental factors and their diversity, it is impossible to predict the future behavior of a complex system with the required accuracy, and even more so without knowledge of its past and the values of the initial conditions. The instability and irreversibility of the processes lead to the destruction of the trajectory of behavior of the SPSS equipment and, consequently, to the possible emergence of a variety of structured collective states. And this threatens the appearance of failures, accidents and catastrophes of equipment of complex complexes. Investigations of instabilities and irreversible processes in complex systems have led to the formation of a coherent theory of using the concept of second (internal) time, both at the microscopic and macroscopic levels of the description of SPSS. Since, due to the random behavior of the trajectories of the equipment of dynamic systems, the internal time differs significantly from astronomical time, it is an operator corresponding to quantities in quantum mechanics. And as a consequence of this, it leads to profound changes at the functional level of the space-time continuum. Strongly unstable systems with a large number of possible irreversible processes are a source of coherence of technological safety phenomena. If, at or near equilibrium, the state of the SPSS equipment, at least for a sufficiently long period of time, is completely determined by boundary conditions, then far from equilibrium, many dissipative structures. That is why in the last three decades of the XX and the beginning of the XXI century, the concepts of deterministic chaos and attractor are used as a generalized parameter of the SSSS. In view of the foregoing, the purpose of this article is to analyze the structure and content of the concept of the operator of internal time in the theory of the durability of complex dynamic systems.
Materials and methods. The conceptual basis of the methodology in the article is the law of increasing entropy and the emergence on its basis of the asymmetry of time in the modes «pastpresent-future.» At the same time, the new concept of “internal time”, which characterizes irreversible processes in unstable dynamic systems, is analyzed. This approach made it possible to obtain analytical expressions of durability indicators based on the new space – time structure: consistent average values of the “age” of systems.
Results. The concept of the application of the concept of “internal time” in the theory of the durability of structurally and functionally complex systems, including for special purposes, is formulated and disclosed. 

Key words

operators of microscopic entropy, Liouville and internal time, durability 

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