A. Renyi's Entropy as a generalization of Basic Processes
https://doi.org/10.21822/2073-6185-2026-53-1-56-63
Abstract
Objective. The aim of the study is to substantiate the possibility of applying A. Renyi's entropy to the problem of analyzing additive and multiplicative growth processes related to complex technical systems.
Method. The Renyi model is proposed, which includes a generalization of the properties inherent in the elements of a complex system and is necessary for the analysis of growth processes. The model includes mathematical expressions for calculating the probabilities of additive and multiplicative growth processes, as well as a generalized equation in a universal form that links both types of growth.
Result. The analysis shows the importance of the obtained values of Renyi entropy depending on the parameter a of the model associated with the growth processes. The performed calculations of the Regnal entropy showed that changing the parameter a makes it possible to expand the range of applied uniformity measures. If the parameter value is assumed to be close to one, therefore, sensitive processes are considered, characterized by subtle differences in the probability distributions of the states of objects. By increasing a, the sensitivity of the estimate decreases, making it possible to identify the largest deviations in the probability distribution. Variation of parameter a is possible provided that different sensitivity levels are selected and is an integral part of changing the structure of the studied set of objects.
Conclusion. The applicability of Shannon entropy is limited to additive processes; Renyi entropy is applicable to the study of complex systems and processes. It is an effective tool for analyzing growth processes, endowed with flexibility in applying sensitivity characteristics in assessing growth changes. By changing the parameter a, it is possible to estimate the heterogeneity of the probability distribution on a set of states of objects with different levels of detail. In particular, the use of The use of Renyi entropy is effective for analyzing the state of technical, economic, and biological systems.
About the Authors
A. S. Dulesov
Katanov State University, Institute of Physics and Technology
Russian Federation
Russian Federation
Alexander S. Dulesov, Dr. Sci. (Eng.), Prof., Prof., Department of Digital Technologies and Design,
92/1 Lenin St., Abakan 655017
D. B. Bayyr
Katanov State University, Institute of Physics and Technology
Russian Federation
Russian Federation
Dolaan B. Bayyr, Postgraduate Student, Department of Digital Technologies and Design,
92/1 Lenin St., Abakan 655017
I. A. Bychkova
Katanov State University, Institute of Physics and Technology
Russian Federation
Russian Federation
Irina A. Bychkova, Master's Student, Department of Digital Technologies and Design,
92/1 Lenin St., Abakan 655017
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For citations:
Dulesov A.S., Bayyr D.B., Bychkova I.A. A. Renyi's Entropy as a generalization of Basic Processes. Herald of Dagestan State Technical University. Technical Sciences. 2026;53(1):56-63. (In Russ.) https://doi.org/10.21822/2073-6185-2026-53-1-56-63
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