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Energy supply is mandatory for the production of economic value.Nevertheless, tradition dictates that an enigmatic 'invisible hand' governseconomic valuation. Physical scientists have long proposed alternative buttestable energy cost theories of economic valuation, and have shown the grosscorrelation between energy consumption and economic output at the nationallevel through input-output energy analysis. However, due to the difficulty ofprecise energy analysis and highly complicated real markets, no decisiveevidence directly linking energy costs to the selling prices of individualcommodities has yet been found. Over the past century, the US metal market hasaccumulated a huge body of price data, which for the first time ever providesus the opportunity to quantitatively examine the direct energy-valuecorrelation. Here, by analyzing the market price data of 65 purified chemicalelements (mainly metals) relative to the total energy consumption for refiningthem from naturally occurring geochemical conditions, we found a clearcorrelation between the energy cost and their market prices. The underlyingphysics we proposed has compatibility with conventional economic concepts suchas the ratio between supply and demand or scarcity's role in economicvaluation. It demonstrates how energy cost serves as the 'invisible hand'governing economic valuation. Thorough understanding of this energy connectionbetween the human economic and the Earth's biogeochemical metabolism isessential for improving the overall energy efficiency and furthermore thesustainability of the human society.

Physical energy cost serves as the ''invisible hand'' governing economic  valuation: Direct evidence from biogeochemical data and the U.S. metal market