Economic Entropy and Sectoral Dynamics: A Thermodynamic Approach to Market Analysis

TL;DR

The paper casts Bogotá’s sports economy as a thermodynamic system, mapping monetary flow to energy and assigning $S$, $T$, and $C$ meaningful economic interpretations. It develops a statistical‑thermodynamics foundation for money, entropy, and heat capacity, and employs Geometrothermodynamics (GTD) to study the equilibrium manifold of sectoral interactions, focusing on $ \,\mathbb{S}_{15}$ (gambling) and $ \,\mathbb{S}_{16}$ (recreation/sports) in 2018–2023. Empirically, $S_{\mathbb{S}_{15}}<S_{\mathbb{S}_{16}}$ and $C_{\mathbb{S}_{16}}>C_{\mathbb{S}_{15}}$, with a heat‑like intersectoral transfer from gambling to recreational sectors; curvature invariants reveal phase‑transition–like crises in the CSDB, offering early warnings and policy‑relevant diagnostics. The framework is extended to incorporate additional sectors and firm counts, showing robust qualitative signals of intersectoral energy redistribution and crisis propensity, and highlighting GTD as a promising tool for prospective economic analysis and public policy design.

Abstract

This paper presents an application of geometrothermodynamics (GTD) to the economic analysis of Bogotá's sports sector through the Satellite Account of Sport (CSDB). By establishing an analogy between thermodynamic systems and economic structures, we develop a mathematical framework where monetary flows behave analogously to energy, while economic entropy, temperature, and heat capacity acquire well-defined economic interpretations. The study focuses on two contrasting sectors: gambling and betting $\mathbb{S}_{15}$, and recreational and sports activities $\mathbb{S}_{16}$, analyzing data from 2018-2023. Our results demonstrate that $\mathbb{S}_{15}$ exhibits lower economic entropy than $\mathbb{S}_{16}$ , indicating a higher degree of organization and regulatory structure in the gambling sector compared to the more heterogeneous recreational sports sector. The heat capacity function reveals critical points that may signal phase transitions in economic dynamics, while Ricci and Kretschmann curvature scalars identify potential crisis points in the sectoral organization. Furthermore, the cross-income elasticity analysis shows distinct resource flow patterns between sectors, suggesting that gambling activities may serve as an economic driver for recreational sports. This thermodynamic approach provides a quantitative tool for analyzing resource redistribution policies and anticipating critical transitions in sectoral economics. The findings suggest that econophysics and statistical thermodynamics constitute powerful frameworks for understanding the sectoral dynamics of Bogotá's sports economy, with significant potential for developing prospective analysis tools in public policy design.

Figures (16)

• Figure 1: Comparison of the entropies of sectors $\mathbb{S}_{15}$ and $\mathbb{S}_{16}$ in the CSDB.
• Figure 2: Comparison of the average money per agent in sectors $\mathbb{S}_{15}$ and $\mathbb{S}_{16}$ of the CSDB.
• Figure 3: Comparison of the heat capacities of sectors $\mathbb{S}_{15}$ and $\mathbb{S}_{16}$ in the CSDB.
• Figure 4: Comparison of $\Delta Q$ for sectors $\mathbb{S}_{15}$ and $\mathbb{S}_{16}$ in the CSDB..
• Figure 5: Comparison of the entropies of sectors $\mathbb{S}_{15}$ and $\mathbb{S}_{16}$ in the CSDB under the extended approximation.