A geometric thermodynamic framework for the analysis of sectoral economic dynamics

This paper investigates the structural stability of the sports economy in Bogotá using the formalism of geometrothermodynamics (GTD). By treating sectoral economic activity as a macroscopic system analogous to a thermodynamic system in equilibrium, the authors aim to identify whether major economic disruptions—specifically the 2020 COVID-19 contraction—induce fundamental changes in the system's underlying equilibrium structure. The researchers construct a Legendre-invariant metric on the manifold of equilibrium states, where the curvature of this manifold serves as a coordinate-independent diagnostic for structural stability and phase transitions.

The study analyzes data from the Sports Satellite Account of Bogotá (CSDB) for the period 2018–2023. By calculating the Ricci and Kretschmann scalars for the equilibrium manifold, the authors demonstrate that these curvature invariants remain finite and regular across the entire empirical range. The 2020 economic contraction, while clearly visible in the raw time series, does not manifest as a curvature singularity in the geometric model. The authors interpret this regularity as evidence that the sectoral system absorbed the macroeconomic shocks of the period without an abrupt reorganization of its equilibrium geometry.

This research extends the application of statistical physics and differential geometry to complex economic systems. By providing a coordinate-invariant measure of equilibrium stability, the GTD framework offers a complementary perspective to standard entropic or macroeconomic indicators. It allows researchers to distinguish between transient fluctuations in economic performance and fundamental structural shifts, providing a rigorous, non-perturbative tool for assessing the resilience of sectoral economic ecosystems.