Investigation of the relationship between the principles of statistical physics and quantum game theories in complex systems

Abstract

The relationship between the principles of statistical physics and quantum game theories is an important object of interdisciplinary research aimed at studying the behavior of complex systems. The interaction of these areas of science expands our knowledge of correlations, dynamics, and optimization in multicomponent systems. The present study focuses on the study of the fundamental relationships between these approaches and their application to modeling complex systems. For this study, we developed a theoretical model that connects the key equations of statistical physics with the principles of quantum game theory. We used standard mathematical modeling methods, such as calculations based on Gibbs distributions, quantum superposition, and game theory methods adapted for multicomponent systems. The numerical Monte Carlo method was also used to test theoretical conclusions. It was found that the mechanisms describing equilibrium and phase transitions in statistical physics are closely related to the formation of strategies and optimization in the framework of quantum games. In particular, it is shown that quantum entangled states can be interpreted as analogs of collective states in statistical physics, which makes it possible to clarify the theoretical limits of price and behavioral decisions in nonlinear systems. The results are confirmed by numerical experiments demonstrating a high degree of agreement between the models and empirical data. The results obtained open up new perspectives for studying complex systems using combined approaches. The possibility of using quantum games to describe collective behavior in physical systems, such as particle dynamics in open systems or neural networks, is revealed. This study provides an understanding of the principles of interaction between statistical physics and quantum game theory, which contributes to the further development of interdisciplinary science and the application of its conclusions to real problems.