Thermodynamic description of world GDP distribution over countries

Abstract

We apply the concept of Rayleigh-Jeans thermalization of classical fields for a description of the world Gross Domestic Product (GDP) distribution over countries. The thermalization appears due to a variety of interactions between countries with conservation of two integrals being total GDP and probability (norm). In such a case there is an emergence of Rayleigh-Jeans condensation at states with low GDP. This phenomenon has been studied theoretically and experimentally in multimode optical fibers and we argue that it is at the origin of emergence of poverty and oligarchic phases for GDP of countries. A similar phenomenon has been discussed recently in the framework of the Wealth Thermalization Hypothesis to explain the high inequality of wealth distribution in human society and companies at Stock Exchange markets. We show that the Rayleigh-Jeans thermalization well describes the GDP distribution during the last 50 years.

Figures (10)

• Figure 1: Lorenz curves of GDP for countries from UN data unyears for 6 years between 1973 and 2023. The $x$-axis corresponds the cumulated fraction of households/countries ($h$) and the $y$-axis to the cumulated fraction of wealth/GDP ($w$).
• Figure 2: Top panel (a): Lorenz curve for the year 1973 from UN data unyears shown by red curve with (+), Gini coefficient is $G=0.892$; WTH theory with RJS model with $\varepsilon(RJS) = 0.0538$ at same $G$ (green curve); RJE model results are shown with blue curve at $\varepsilon(RJE) = 0.00888$, $a=4.301$; bottom panel (b) shows same style data for the year 2023 with $G=0.88$, $\varepsilon(RJS) = 0.0601$ for the RJS model and $\varepsilon(RJE) = 0.01$, $a=4.31$ for the RJE model. Parameters $T$, $\mu$ for RJS and RJE models for year 2023 at $N=212$ are given in SupMat.
• Figure 3: Color plot of wealth $w$ from Lorenz curves for the from the RJE model at $a=4.31$. The $x$-axis corresponds to the fraction of households $h\in[0, 1]$ and the $y$-axis to the rescaled energy $\varepsilon\in[0, \varepsilon_C[$ where $\varepsilon_C=0.218$ is the critical value at which the transition from $T>0$ to $T<0$ appears. The ticks mark integer multiples of 0.1 for $h$ and $\varepsilon$. The white line corresponds to $\varepsilon(RJE)=0.01$ obtained from the fit of the RJE model using the GDP data of 2023 shown in Fig. \ref{['fig2']}.
• Figure 4: The Lorenz curve for SE market capitalization of $N=113$ countries, data from marketcap. The Lorenz curves are shown in the same style as in Fig. \ref{['fig2']}. Here $G=0.895$, $\varepsilon(RJS) =0.0525$ for the RJS model, $\varepsilon(RJE) =0.0119$, $a=3.721$ for the RJE model.
• Figure 5: As Fig. \ref{['fig3']} with $a=3.721$, $\varepsilon_C=0.244$ and a white line at $\varepsilon(RJE)=0.0119$ obtained from the fit of the RJE model using the SE Market Cap data shown in Fig. \ref{['fig4']}.