A new monetary metric is found in the thermodynamic relation between energy and GDP

Brian P. Hanley

Papers from arXiv.org

Abstract: A robust thermodynamic relation between inflation corrected monetary valuation and energy emerges from existing work. This is based on the energy used, the aggregate efficiency of all production processes ($\Lambda(t)$) in terms of Joules per dollar of gross world product, and the gross world product: $\frac{E_A(t) \text{[J]}}{\Lambda(t) \text{[J/\$]}} = Y(t) [\$]$ where: J = Joules, \$= currency. This directs us to the production system and all of its processes in addition to alternatives to carbon energy. The original relation appeared in 'Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?' (Garrett 2011). There a foundation assumption was made that a variable $\lambda$ representing energy per dollar would disprove the presented model. However, because $\lambda$ has dimension [$\frac{E}{\$ \; GWP}$], it represents the aggregate efficiency of all global production, and cannot be a constant in an economic model. Thus, aggregate production efficiency is: $\Lambda(t) \equiv \sum {\lambda_i(t) \cdot \frac{P_i}{GWP}}$. The claimed 50 year constant relation of $W$ ($\sum_{i = n}^{t} Y_i \text{ [\$]}$) to the energy $E$ of the final year is incorrect -- the relation is not flat, nor should this be expected. The graph of $W$ from 1970 back in time is shown to have an historic minimum in 1970 driven by growth in energy consumption and increasing efficiency of energy use that is unlikely to be repeated. With improvements, a robust thermodynamic model is obtained that has general application to the relationship between money and energy and may be useable for evaluating the health of currencies and economies.

Date: 2025-08, Revised 2026-04
New Economics Papers: this item is included in nep-ene, nep-env and nep-mac
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