The Persistence Coefficient: GDP as a measure of capital turnover speed, not wealth: evidence from Spanish regions and the EU-27

Standard macroeconomic metrics treat capital accumulation as wealth creation. This paper introduces the Persistence Coefficient (Φ), a time-integrated measure of the useful service delivered by a stock of capital, defined as the product of energy return (Value of Thermodynamic Return, VTR) and temporal return (Temporal Rate of Return, TRT) integrated over the asset's functional life. We derive Φ axiomatically, showing it is the unique metric satisfying four minimal coherence properties. We then derive a theoretical prediction from the structure of GDP itself: since GDP measures transactions per unit time, and transaction frequency is the inverse of product lifetime, GDP is structurally proportional to the inverse of mean capital persistence (GDP ∝ 1/TRT). We test this prediction empirically across six independent tests using official data from Spanish regions and EU-27 member states, finding strong and consistent results. The implication is direct: economies with higher GDP per capita are not wealthier in any physical sense — they rotate their capital stock faster.