Entropic characterization of Gross Domestic Product per capita (GDP) values of countries

Abstract

The historical change of Gross Domestic Product per capita (GDP) values of countries with the thirty largest economies was analyzed by using different entropies, (i) topological entropy, (ii) Shannon entropy, and (iii) configurational entropy. Topological entropy was used to analyze the number of periodic points of each ranking, and five segments corresponded to economic crises in the first ranking. The behavior in each segment could be described by polynomial equations. In all other rankings, the segments distorted to varying extents. Shannon entropy was used to analyze the entropy of each ranking and also the yearly change of the entropy of each country from 1960 to 2020. The negentropy change of each country was also analyzed. By the end of 2020, one country had equal entropy and negentropy, twelve countries had larger, and seventeen countries had smaller entropies than their negentropy. There was a close similarity between the change of topological entropy and negentropy in any ranking, but topological entropy gave more precise information because it is dependent not only on the distribution of data but also on the sequence of GDP data of different countries. The 18th ranking was a critical ranking having very large topological entropy and negentropy. The GDPs of countries sharply dropped after the 18th ranking. The configurational entropy came out to be maximum at the minimum values of GDP, or vice versa. It usually started with a small negative value, and its magnitude became larger in time. However, there occurred severe fluctuations in many of the cases. It means the configurational entropy gets less negative (i.e. it increases) in time through fluctuations. Overall, the entropic analysis of the GDP values of countries provides quantitative information about how countries performed over the years. The methods used here can be applied to other time-series systems having similar dynamics to GDP, as well as to competitive systems.