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arxiv: 2508.08723 · v2 · submitted 2025-08-12 · 💰 econ.GN · q-fin.EC

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

Brian P. Hanley This is my paper

Pith reviewed 2026-05-18 23:39 UTC · model grok-4.3

classification 💰 econ.GN q-fin.EC
keywords thermodynamic relationenergy and GDPaggregate efficiencygross world productmonetary valuationeconomic healthproduction processesinflation correction
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The pith

GDP equals total energy divided by the aggregate efficiency of all production processes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives a thermodynamic equation in which energy consumed divided by a changing aggregate efficiency of turning energy into value equals the inflation-corrected gross world product. It replaces an earlier assumption of constant efficiency with a weighted sum across all processes and shows that cumulative output reaches a minimum around 1970 rather than staying flat. A sympathetic reader would care because the relation grounds monetary value in physical energy flows and offers a potential new way to judge the condition of currencies and economies.

Core claim

The central claim is that the equation E_A(t) [J] / Λ(t) [J/$] = Y(t) [$] gives a robust relation between energy and inflation-corrected monetary valuation, where Λ(t) is the aggregate efficiency of global production defined as the weighted sum of individual process efficiencies. The paper shows that the cumulative sum of output does not hold a constant relation to final-year energy and instead exhibits a minimum in 1970 driven by efficiency gains and energy growth. With these corrections the model becomes usable for the general relationship between money and energy.

What carries the argument

Aggregate efficiency Λ(t) defined as the weighted sum of individual process efficiencies, which converts total energy input into monetary output value.

If this is right

  • The model directs focus to the full production system and alternatives to carbon energy sources.
  • The previously claimed constant 50-year relation between cumulative output and energy is shown to be incorrect and time-varying.
  • The relation may be used to evaluate the health of currencies and economies.
  • Improvements produce a robust thermodynamic model with general application to money-energy links.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying the same accounting at national scale could expose differences in how efficiently economies convert energy into output.
  • Tracking long-term shifts in aggregate efficiency might flag structural changes before they register in conventional financial indicators.
  • Linking this framework to carbon-emission projections could add physical bounds to estimates of future economic growth.

Load-bearing premise

The aggregate efficiency can be calculated from historical data without circular dependence on the GDP values it is meant to explain, and the 1970 minimum is not an artifact of the chosen starting year or data exclusions.

What would settle it

Recalculation of aggregate efficiency from alternative historical datasets or different base years that eliminates the 1970 minimum would show the claimed relation does not hold.

Figures

Figures reproduced from arXiv: 2508.08723 by Brian P. Hanley.

Figure 1
Figure 1. Figure 1: Here dotted red curves are either Lotka′ s W heel (LW) datasets, or created from them. Dashed gold curves are special datasets also from Lotka’s Wheel supplement. Solid black curves are the author’s replicates. Panel A Dotted red curve is YLW (GWP). Solid black curve YRep is the interpolated composite. YRep is reasonably close, so this is not a primary reason for a large discrepancy. Panel B. W summation c… view at source ↗
Figure 2
Figure 2. Figure 2: Curves extended back to -14,000 CE using Morris tables (Morris, 2013, pp. 55, 61, 68, 111,). Population is always the over￾whelming influence. Panel A. YRepMorris curve is estimated GWP from -14,000 to 2019 CE. Panel B. W curves. WRepMorris is the summation from -14,000 to 2019 CE utilizing the Geary-Khamis dollar kCal method pegged to year 1 CE. WLW is the supplement dataset of Lotka′ s W heel from 1 CE f… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a thermodynamic relation E_A(t)/Λ(t) = Y(t) between energy consumption and gross world product, where Λ(t) is defined as the share-weighted sum of individual process efficiencies Λ(t) ≡ ∑ λ_i(t) · (P_i/GWP). It argues that the previously claimed constant 50-year relation between cumulative wealth W and energy is incorrect, instead showing a minimum around 1970 driven by energy consumption growth and efficiency improvements, and positions the framework as applicable to evaluating currency and economy health.

Significance. If the relation can be established as non-tautological with independent data sources and the 1970 minimum shown to be robust rather than an artifact, the work would offer a physically motivated link between monetary valuation and energy flows with potential utility for sustainability and economic diagnostics beyond standard models. The reinterpretation of Garrett (2011) provides a clear point of departure.

major comments (2)
  1. [Abstract, defining equation] Abstract, defining equation: The relation E_A(t)/Λ(t) = Y(t) is presented as a substantive thermodynamic link, but Λ(t) is constructed using P_i/GWP terms drawn from the same production and GWP aggregates that define Y(t). The manuscript must provide an explicit protocol showing how individual λ_i(t) and P_i are obtained from energy/process data independent of aggregate GWP or Y; absent this, the equality reduces to a definitional identity and the claimed robustness does not follow.
  2. [Abstract] Abstract: The assertion that the 50-year constant W-E relation is incorrect and that a historic minimum occurs in 1970 is load-bearing for the central correction to prior work, yet no derivation steps, data sources, error analysis, or sensitivity tests to starting year or sector exclusions are supplied. This leaves open whether the extremum is physically driven or data-selection dependent.
minor comments (2)
  1. The summation limits for W = ∑_{i=n}^t Y_i should be defined explicitly, including the choice of starting index n and its justification.
  2. Notation for dimensions ([J], [J/$], [$]) is clear but could be repeated in any subsequent equations for consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We address each of the major comments below and outline the revisions we will make to improve the clarity and robustness of our arguments.

read point-by-point responses

  1. Referee: [Abstract, defining equation] The relation E_A(t)/Λ(t) = Y(t) is presented as a substantive thermodynamic link, but Λ(t) is constructed using P_i/GWP terms drawn from the same production and GWP aggregates that define Y(t). The manuscript must provide an explicit protocol showing how individual λ_i(t) and P_i are obtained from energy/process data independent of aggregate GWP or Y; absent this, the equality reduces to a definitional identity and the claimed robustness does not follow.

    Authors: We agree that the independence of the components needs to be made explicit to avoid any perception of tautology. The individual efficiencies λ_i(t) are obtained from detailed process-level data on energy consumption and output for specific sectors, while P_i are the value-added contributions from national accounts and industry reports, which are compiled independently of the aggregate energy totals used for E_A(t). We will revise the manuscript to include a dedicated subsection describing the data sources and calculation protocol for Λ(t), ensuring the non-tautological nature is clear. revision: yes

  2. Referee: [Abstract] The assertion that the 50-year constant W-E relation is incorrect and that a historic minimum occurs in 1970 is load-bearing for the central correction to prior work, yet no derivation steps, data sources, error analysis, or sensitivity tests to starting year or sector exclusions are supplied. This leaves open whether the extremum is physically driven or data-selection dependent.

    Authors: We acknowledge the need for greater transparency in the derivation of the 1970 minimum. The cumulative wealth W is computed as the sum of historical Y(t) from available economic data, combined with energy consumption series. The minimum arises from the interplay of increasing E_A(t) and improving Λ(t). In the revised version, we will add explicit derivation steps, cite the specific data sources used in our analysis, include error bars or uncertainty estimates, and perform sensitivity analyses varying the start year and excluding certain sectors to demonstrate robustness. revision: yes

Circularity Check

1 steps flagged

Λ(t) definition reduces E_A/Λ = Y to a definitional identity

specific steps
  1. self definitional [Abstract]
    "This is based on the energy used, the aggregate efficiency of all production processes (Λ(t)) in terms of Joules per dollar of gross world product, and the gross world product: E_A(t) [J] / Λ(t) [J/$] = Y(t) [$] ... Thus, aggregate production efficiency is: Λ(t) ≡ ∑ λ_i(t) · (P_i/GWP)."

    GWP is defined as gross world product Y(t). With λ_i as energy per dollar of production for process i, E_A(t) = ∑ λ_i(t) P_i holds by construction. The weighting then gives Λ(t) = [∑ λ_i P_i]/GWP = E_A(t)/Y(t). Substituting back yields Y(t) = E_A(t) / (E_A(t)/Y(t)), which is the identity Y(t) = Y(t).

full rationale

The paper presents the core relation as a thermodynamic link usable for evaluating economies, but the aggregate efficiency Λ(t) is explicitly defined using production shares normalized by GWP (i.e., Y(t)). When λ_i are taken as energy-per-dollar for individual processes, total energy E_A equals the sum of λ_i P_i by definition. Substituting the weighting then forces Λ(t) = E_A(t)/Y(t), collapsing the claimed equality into Y(t) = Y(t). This is a self-definitional reduction rather than an independent derivation; the 1970 minimum and currency-health claims inherit the same dependence on the monetary aggregates they purport to explain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on re-expressing the prior efficiency term as a weighted sum and on the empirical claim of a 1970 minimum; no new physical constants or entities are introduced.

axioms (2)
  • domain assumption Aggregate efficiency Λ(t) is exactly the share-weighted sum of individual process efficiencies λ_i(t)
    Stated in the abstract as Λ(t) ≡ ∑ λ_i(t) · P_i / GWP
  • domain assumption The graph of cumulative output W back to 1970 exhibits a minimum driven by energy growth and efficiency gains
    Claimed without showing the underlying series or exclusion rules

pith-pipeline@v0.9.0 · 5865 in / 1434 out tokens · 40991 ms · 2026-05-18T23:39:21.763301+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Barnett, W.: Dimensions and economics: Some problems, The Quarterly Journal of Austrian Economics, 6, 27–46, https://doi.org/10.1007/s12113-003-1022-2,

    work page doi:10.1007/s12113-003-1022-2

  2. [2]

    S., Yellen, J

    Brooks, A. S., Yellen, J. E., Potts, R., Behrensmeyer, A. K., Deino, A. L., Leslie, D. E., Ambrose, S. H., Ferguson, J. R., d’Errico, F., Zipkin, A. M., Whittaker, S., Post, J., Veatch, E. G., Foecke, K., and Clark, J. B.: Long-distance stone transport and pigment use in the earliest Middle Stone Age, Science, 360, 90–94, https://doi.org/10.1126/science.aao2646,

    work page doi:10.1126/science.aao2646

  3. [3]

    Chang, Y .-L. K., Miyazawa, Y ., Guo, X., Varlamov, S., Yang, H., and Kaifu, Y .: Traversing the Kuroshio: Paleolithic migration across one of the world’s strongest ocean currents, Science Advances, 11, eadv5508, https://doi.org/10.1126/sciadv.adv5508,

    work page doi:10.1126/sciadv.adv5508

  4. [4]

    C., Drysdale, R

    Corrick, E. C., Drysdale, R. N., Hellstrom, J. C., Capron, E., Rasmussen, S. O., Zhang, X., Fleitmann, D., Couchoud, I., and Wolff, E.: Syn- chronous timing of abrupt climate changes during the last glacial period, Science, 369, 963–969, https://doi.org/10.1126/science.aay5538,

    work page doi:10.1126/science.aay5538

  5. [5]

    De Almeida, A. T., T. E. Ferreira, F. J., and Fong, J. A.: Standards for Efficiency of Electric Motors, IEEE Industry Applications Magazine, 17, 12–19, https://doi.org/10.1109/MIAS.2010.939427,

    work page doi:10.1109/mias.2010.939427 2010

  6. [6]

    and Heston, A.: Understanding PPPs and PPP-Based National Accounts., American Economic Journal: Macroeconomics, 2, 1–35, https://doi.org/https://doi.org/10.1257/mac.2.4.1,

    Deaton, A. and Heston, A.: Understanding PPPs and PPP-Based National Accounts., American Economic Journal: Macroeconomics, 2, 1–35, https://doi.org/https://doi.org/10.1257/mac.2.4.1,

    work page doi:10.1257/mac.2.4.1

  7. [7]

    Duenhaupt, P.: Financialization and the rentier income share – evidence from the USA and Germany, International Review of Applied Economics, 26, 465–487, https://doi.org/10.1080/02692171.2011.595705,

    work page doi:10.1080/02692171.2011.595705 2011

  8. [8]

    D.: Historical Estimates of World Population: An Evaluation, Population and Development Review, 3, 253–296, http://www.jstor

    Durand, J. D.: Historical Estimates of World Population: An Evaluation, Population and Development Review, 3, 253–296, http://www.jstor. org/stable/1971891,

    work page arXiv

  9. [9]

    Dyvik, EH: Estimated 359 million companies worldwide in 2023, increased from 2020’s 328 million companies., https://www.statista.com/ study/102571/companies-worldwide/ Accessed: 2025-02-12,

    work page 2023

  10. [10]

    Felipe, J. and McCombie, J.: The illusions of calculating total factor productivity and testing growth models: from Cobb-Douglas to Solow and Romer, Journal of Post Keynesian Economics, 43, 470–513, https://doi.org/10.1080/01603477.2020.1774393,

    work page doi:10.1080/01603477.2020.1774393 2020

  11. [11]

    Louis Federal Reserve Bank: FRED Gross Domestic Product for World (NYGDPMKTPCDWLD), https://fred.stlouisfed.org/ series/NYGDPMKTPCDWLD, accessed 2024-02-29.,

    FRED, St. Louis Federal Reserve Bank: FRED Gross Domestic Product for World (NYGDPMKTPCDWLD), https://fred.stlouisfed.org/ series/NYGDPMKTPCDWLD, accessed 2024-02-29.,

    work page 2024

  12. [12]

    A., Robinson, E., Byers, D

    Freeman, J., Baggio, J. A., Robinson, E., Byers, D. A., Gayo, E., Finley, J. B., Meyer, J. A., Kelly, R. L., and Anderies, J. M.: Synchronization of energy consumption by human societies throughout the Holocene, Proceedings of the National Academy of Sciences, 115, 9962–9967, https://doi.org/10.1073/pnas.1802859115,

    work page doi:10.1073/pnas.1802859115

  13. [13]

    W.: The Evolution of Creditary Structures and Controls, Palgrave Macmillan UK, London, ISBN 978-1-349-54156-0, https://doi.org/10.1057/9780230288447,

    Gardiner, G. W.: The Evolution of Creditary Structures and Controls, Palgrave Macmillan UK, London, ISBN 978-1-349-54156-0, https://doi.org/10.1057/9780230288447,

    work page doi:10.1057/9780230288447

  14. [14]

    J.: Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?, Climatic Change, 104, 437–455, https://doi.org/10.1007/s10584-009-9717-9,

    Garrett, T. J.: Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?, Climatic Change, 104, 437–455, https://doi.org/10.1007/s10584-009-9717-9,

    work page doi:10.1007/s10584-009-9717-9

  15. [15]

    J.: Modes of growth in dynamic systems, Proceedings of the Royal Society A, 468, 2352–2549, https://doi.org/http://doi.org/10.1098/rspa.2012.0039, 2012a

    Garrett, T. J.: Modes of growth in dynamic systems, Proceedings of the Royal Society A, 468, 2352–2549, https://doi.org/http://doi.org/10.1098/rspa.2012.0039, 2012a. Garrett, T. J.: No way out? The double-bind in seeking global prosperity alongside mitigated climate change, Earth System Dynamics, 3, 1–17, https://doi.org/10.5194/esd-3-1-2012, 2012b. Garre...

    work page doi:10.1098/rspa.2012.0039 2012

  16. [16]

    Physical basis, Earth’s Future, 2, 127–151, https://doi.org/https://doi.org/10.1002/2013EF000171,

    work page doi:10.1002/2013ef000171

  17. [17]

    J.: Long-run evolution of the global economy – Part 2: Hindcasts of innovation and growth, Earth System Dynamics, 6, 673–688, https://doi.org/10.5194/esd-6-673-2015,

    Garrett, T. J.: Long-run evolution of the global economy – Part 2: Hindcasts of innovation and growth, Earth System Dynamics, 6, 673–688, https://doi.org/10.5194/esd-6-673-2015,

    work page doi:10.5194/esd-6-673-2015 2015

  18. [18]

    J., Grasselli, M

    Garrett, T. J., Grasselli, M. R., and Keen, S.: Lotka’s wheel and the long arm of history: how does the distant past determine today’s global rate of energy consumption?, Earth System Dynamics, 13, 1021–1028, https://doi.org/10.5194/esd-13-1021-2022,

    work page doi:10.5194/esd-13-1021-2022 2022

  19. [19]

    R., Sousa, V ., Cabello Eras, J

    Gómez, J. R., Sousa, V ., Cabello Eras, J. J., Sagastume Gutiérrez, A., Viego, P. R., Quispe, E. C., and de León, G.: Assessment criteria of the feasibility of replacement standard efficiency electric motors with high-efficiency motors, Energy, 239, 121 877, https://doi.org/https://doi.org/10.1016/j.energy.2021.121877,

    work page doi:10.1016/j.energy.2021.121877 2021

  20. [20]

    Haub, C.: How many people have ever lived on earth?, Population today, 23, 4–5, https://pubmed.ncbi.nlm.nih.gov/12288594/,

    work page arXiv

  21. [21]

    S., d’Errico, F., van Niekerk, K

    Henshilwood, C. S., d’Errico, F., van Niekerk, K. L., Coquinot, Y ., Jacobs, Z., Lauritzen, S.-E., Menu, M., and García-Moreno, R.: A 100,000- Year-Old Ochre-Processing Workshop at Blombos Cave, South Africa, Science, 334, 219–222, https://doi.org/10.1126/science.1211535,

    work page doi:10.1126/science.1211535

  22. [22]

    Hu, W., Hao, Z., Du, P., Vincenzo, F. D., Manzi, G., Cui, J., Fu, Y .-X., Pan, Y .-H., and Li, H.: Genomic inference of a severe human bottleneck during the Early to Middle Pleistocene transition, Science, 381, 979–984, https://doi.org/10.1126/science.abq7487,

    work page doi:10.1126/science.abq7487

  23. [23]

    III, W.: Climate Change 2007, Tech. rep., Intergovernmental panel on climate change (IPCC), Geneva, Switzerland, https://archive.ipcc.ch/ publications_and_data/ar4/wg3/en/ch3s3-2-1-4.html, note: 3.2.1.4 The use of MER in economic and emissions scenarios modelling. “On the question of whether PPP or MER should be employed in economic scenarios, the general...

    work page 2007

  24. [24]

    Institute for Global Sustainability: Maximum efficiencies of engines and turbines 1700-2000, #https://visualizingenergy.org/ maximum-efficiencies-of-engines-and-turbines-1700-2000/ Accessed: 2025-05-10,

    work page 2000

  25. [25]

    U., and Standish, R.: A Note on the Role of Energy in Production, Ecological Economics, 157, 40–46, https://doi.org/10.1016/j.ecolecon.2018.11.002,

    Keen, S., Ayres, R. U., and Standish, R.: A Note on the Role of Energy in Production, Ecological Economics, 157, 40–46, https://doi.org/10.1016/j.ecolecon.2018.11.002,

    work page doi:10.1016/j.ecolecon.2018.11.002 2018

  26. [26]

    Klein Goldewijk, K., Beusen, A., van Drecht, G., and de V os, M.: The HYDE 3.1 spatially explicit database of human-induced global land-use change over the past 12,000 years, Global Ecology and Biogeography, 20, 73–86, https://doi.org/https://doi.org/10.1111/j.1466- 8238.2010.00587.x,

    work page doi:10.1111/j.1466- 2010

  27. [27]

    G.: The Transparency International Corruption Perceptions Index 1999 — Framework Document, https://images

    Lambsdorff, J. G.: The Transparency International Corruption Perceptions Index 1999 — Framework Document, https://images. transparencycdn.org/images/1999_CPI_Framework_EN.pdf Accessed: 2025-02-08,

    work page 1999

  28. [28]

    J., Bierman, R

    19 Li, L., Comi, T. J., Bierman, R. F., and Akey, J. M.: Recurrent gene flow between Neanderthals and modern humans over the past 200,000 years, Science, 385, eadi1768, https://doi.org/10.1126/science.adi1768,

    work page doi:10.1126/science.adi1768

  29. [29]

    Mafessoni, F. and Prüfer, K.: Better support for a small effective population size of Neandertals and a long shared history of Neandertals and Denisovans, Proceedings of the National Academy of Sciences, 114, E10 256–E10 257, https://doi.org/10.1073/pnas.1716918114,

    work page doi:10.1073/pnas.1716918114

  30. [30]

    Morris, I.: The Measure of Civilization: How Social Development Decides the Fate of Nations, Princeton University Press, ISBN 9780691155685, url=https://press.princeton.edu/books/hardcover/9780691155685/the-measure-of-civilization,

    work page arXiv

  31. [31]

    Nussbaum, A.: The Law of the Dollar, Columbia Law Review, 37, 1057–1091, http://www.jstor.org/stable/1116782,

    work page arXiv

  32. [32]

    Global GDP over the long run – World Bank, Maddison Project Database, Maddison Database – Historical data

    Our World in Data: Global GDP over the long run, https://ourworldindata.org/grapher/population, accessed 2024-08-24., 2023a. Our World in Data: Global GDP over the long run, world Bank (2023); Bolt and van Zanden - Maddison Project Database 2023; Maddi- son Database 2010 – with major processing by Our World in Data. “Global GDP over the long run – World B...

    work page doi:10.1126/sciadv.adn8129 2024

  33. [33]

    Rosling, O., Ronnlund, A., Ingebire, D., Sanchez, C., Day, L., and Zia, T.: Global population, https://www.gapminder.org/data/ Accessed: 2023-05-12,

    work page 2023

  34. [34]

    V ., Grimm, S

    Schmidt, I., Gehlen, B., Winkler, K., Arrizabalaga, A., Arts, N., Bicho, N., Crombé, P., Eriksen, B. V ., Grimm, S. B., Kapustka, K., Langlais, M., Mevel, L., Naudinot, N., Nerudová, Z., Niekus, M., Peresani, M., Riede, F., Sauer, F., Schön, W., Sobkowiak-Tabaka, I., Vandendriess- che, H., Weber, M.-J., Zander, A., Zimmermann, A., and Maier, A.: Large sca...

    work page doi:10.1371/journal.pone.0310942

  35. [35]

    Perfect absorption in complex scattering systems with or without hidden symmetries,

    Shipton, C., Roberts, P., Archer, W., Armitage, S. J., Bita, C., Blinkhorn, J., Courtney-Mustaphi, C., Crowther, A., Curtis, R., Errico, F. d., Douka, K., Faulkner, P., Groucutt, H. S., Helm, R., Herries, A. I. R., Jembe, S., Kourampas, N., Lee-Thorp, J., Marchant, R., Mercader, J., Marti, A. P., Prendergast, M. E., Rowson, B., Tengeza, A., Tibesasa, R., ...

    work page doi:10.1038/s41467-

  36. [36]

    549–561, Elsevier, ISBN 9780121764807, available: https://vaclavsmil.com/wp-content/uploads/docs/smil-article-2004world-history-energy.pdf, accessed 2024-04-15,

    Smil, V .: World history and energy., in: Encyclopedia of Energy, edited by Cleveland, C., pp. 549–561, Elsevier, ISBN 9780121764807, available: https://vaclavsmil.com/wp-content/uploads/docs/smil-article-2004world-history-energy.pdf, accessed 2024-04-15,

    work page 2024

  37. [37]

    United States Census Bureau: Historical Estimates of World Population, https://www.census.gov/data/tables/time-series/demo/ international-programs/historical-est-worldpop.html, accessed 2024-08-20.,

    work page 2024