Thermostatistical Evaluation of Economic Activity

We presented an analysis of Bogotá's sports sector through the lens of thermostatistical models applied to economic systems. The study explores the cross-price elasticity of Income (λ) to assess whether sports services in Bogotá are perceived as normal or inferior goods. By examining data from the Sports Satellite Account of Bogotá (CSDB) from 2018 to 2022, we found that the demand for sports services was highly elastic, especially in years when the economy improved, implying that these services are viewed as normal or luxury goods. Additionally, the partition function, entropy, and heat capacity of the economic system are calculated, revealing that the entropy is consistent with the Boltzmann Principle. This indicates a strong correlation between the system's microstates and its macroeconomic state, supporting the statistical thermodynamic framework used. The study also applies geometrothermodynamics to evaluate the system's stability, utilizing Kretschmann and Ricci scalars to uncover economic singularities or crises. These singularities coincide with the pandemic period, reflecting its disruptive impact on the sector. This integration of geometric thermodynamics offers a deep interpretation of the system’s stability, revealing how external shocks, such as COVID-19, cause measurable disturbances in the economic structure. The analysis shows that Bogotá's sports sector responds elastically to changes in GDP, and its stability is influenced by various macroeconomic factors. However, the decrease in the heat capacity of the system as the economic temperature rises suggests potential growth limitations, making further research essential to fully understand the sector's long-term prospects.