A technological capability scale for civilizations from the Kardashev and Barrow scales

Abstract:We introduce a technological capability scale that ranks civilizations by the control operations they can perform per second. A control operation is defined as setting one binary degree of freedom of matter to a specified value, whatever its previous state. Building on constructor theory, we sort them into construction and its special cases on information media, namely processing, storage and transfer. The index $\Xi = K + B$ adds to the Kardashev index $K$ an efficiency index $B$ of energy per operation, measured from the thermal floor at the microwave background temperature. The Kardashev scale gives the ceiling for resets of thermally random bits with heat radiated into the present sky, and the Barrow scale gives the floor, which for such a reset is the thermal floor at the heat-rejection temperature at every level. Since 1950 the energy per logic operation has fallen 11.7 orders of magnitude, around 5 through miniaturization. Humanity, at $K = 0.73$, computes with CMOS logic gates at $B = -0.78$ in primary energy. We describe the ultimate technology, at $\Xi = 7.58$, which would dissipate the conjectured largest power $c^5/4G$ into an uncharged, non-rotating black hole near its largest mass in de Sitter space.

22 pages, 3 figures, 4 tables. Electronic supplementary material of 56 pages, with 3 figures and 3 tables, and code are ancillary files

Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); Physics and Society (physics.soc-ph)

arXiv:2609.35237 [quant-ph]

(or arXiv:2609.35237v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.35237 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

code/figures/make_figures.py

code/figures/make_figures_output.txt

code/figures/write_systems_table.py

code/tables/fig4_points.json

code/tables/make_table4.py

electronic-supplementary-material.pdf

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