Interpretation and Applications of Non-Extensive Statistics of Complex Systems: From Gravitating and Quantum System to Financial Liquidity Providing

Non-extensive statistics is a form of statistics that differs from the usual statistics in the sense that certain quantities that are derived from independent systems (for example, Tsallis entropy) may not combine together into the total quantity of the whole in a straightforward manner, and an average of a quantity may not be calculated by the usual arithmetic mean (for example, Rényi entropy). This statistical feature is interesting because it has been found to explain many complex phenomena in nature, such as those related to black holes and atomic systems at extremely low temperatures, more accurately than using normal statistics. It was also found that non-extensive statistics can be used to describe complex relationships in some man-made systems such as capital markets. However, at present, the understanding of the actual meaning of non-extensive statistics is still incomplete. This certainly affects the reliability of the various applications mentioned above. The aims of this project are to find more understanding of the meaning of non-extensive statistics and its implications by constructing and studying mathematical models that are related to the thermodynamic behavior of black holes, quantum multiparticle systems, and the liquidity of the financial market, which are examples of both natural and man-made complex systems. The researchers hope that the results of this study will contribute to the understanding and confidence in the use of this statistics in broader contexts, such as in the applications with artificial intelligence and data science.