标题： 经济熵与部门动态：市场分析的热力学方法 显示英文标题

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

摘要： 本文将几何热力学（GTD）应用于波哥大的体育部门经济分析，通过体育卫星账户（CSDB）进行研究。 通过建立热力学系统与经济结构之间的类比，我们开发了一个数学框架，其中货币流动行为类似于能量，而经济熵、温度和热容量则获得明确的经济解释。 本研究重点关注两个对比部门：博彩和投注$\mathbb{S}_{15}$，以及休闲和体育活动$\mathbb{S}_{16}$，分析2018-2023年的数据。 我们的结果表明，$\mathbb{S}_{15}$的经济熵低于$\mathbb{S}_{16}$，表明博彩部门相比更加异质的休闲体育部门具有更高的组织程度和监管结构。 热容量函数揭示了可能在经济动态中表示相变的关键点，而里奇和克雷茨曼曲率标量则识别出部门组织中的潜在危机点。 此外，交叉收入弹性分析显示部门间资源流动模式存在显著差异，表明博彩活动可能作为休闲体育的经济驱动力。 这种热力学方法为分析资源再分配政策和预测部门经济学中的关键转变提供了定量工具。 研究结果表明，经济物理学和统计热力学构成了理解波哥大体育经济部门动态的强大框架，并在公共政策设计中开发前瞻性分析工具方面具有重大潜力。 显示英文摘要

摘要： This paper presents an application of geometrothermodynamics (GTD) to the economic analysis of Bogot\'a'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 Bogot\'a's sports economy, with significant potential for developing prospective analysis tools in public policy design.