Investigation on Thermodynamic Entropy in Quantum Statistics for Stock Market Networks

The stock market is a dynamic mechanism consisting of complex interactions between financial entities, such as banks, companies and institutions. The network structure can be used to depict such a complex interactive device. A time-developing network between companies and individuals is formed by the underlying stock exchange system, which characterises stock price correlations in time-sequential trades. Here, in quantum statistics, we are developing a novel technique to evaluate the growth of the financial market. In the heat bath analogy, we analyse the thermodynamic entropy where the normalised Laplacian matrix plays the function of the Hamiltonian network operator. The Hamiltonian eigenvalues determine the energy levels of the network that are occupied by either indistinguishable bosons or fermions that comply with the exclusion principle of Pauli. This offers partition functions related to statistics from Bose-Einstein and Fermi-Dirac. We perform experiments to demonstrate that thermodynamic entropy can reflect the evolution of the network and consider the considerable variance during the financial crisis in the network structure. This thermodynamic characterization offers an excellent basis for describing the stock market’s variations.

Author(s) Details

Dr. Jianjia Wang
School of Computer Engineering and Science, Shanghai University, 200444, P.R. China and Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, P.R. China.

Chenyue Lin
Department of Mathematics and Statistics, Queen’s University, K7L 3N6, Canada.

Yilei Wang
State Grid Nanjing Power Supply Company, State Grid Corporation of China, Nanjing, 210019, P.R. China.

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