Abstract

We develop a geometric thermodynamic framework for the analysis of sectoral economic dynamics grounded in statistical physics principles. By constructing a Legendre-invariant thermodynamic metric within the formalism of geometrothermodynamics (GTD), we establish a minimal effective structure consistent with extensivity and entropy-based representations of macroscopic economic systems. The resulting thermodynamic curvature provides a coordinate-independent measure of structural interactions and equilibrium stability across economic sectors. Applying this framework to satellite account data, we find that the thermodynamic curvature of the equilibrium manifold remains finite and regular across the empirically relevant range, with no curvature singularity in the period studied. In particular, the 2020 contraction—the most pronounced macroeconomic disruption in the sample—is not reflected as a curvature singularity in the equilibrium geometry. We read this regularity as a diagnostic of structural stability: the sectoral system absorbs such disruptions without an abrupt reorganisation of its equilibrium geometry. The geometric invariants thus capture stability properties not directly accessible through standard entropic indicators alone, offering a complementary statistical description of economic dynamics. Our results demonstrate that thermodynamic geometry furnishes a consistent bridge between entropy-based macroeconomic modelling and coordinate-invariant measures of equilibrium stability, extending the applicability of geometric methods in statistical physics to complex economic systems.

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