precision costs dissipation. for any current $J$ in a steady non-equilibrium state,
$$\frac{\mathrm{Var}(J)}{\langle J\rangle^2} \;\ge\; \frac{2k_B}{\Sigma}$$
where $\Sigma$ is the entropy produced. halving the relative error of any measurement, clock, or motor costs at least four times the dissipation (Barato–Seifert 2015; verified in colloidal and single-electron systems)
the consequence for cyber is not decorative. settlement estimates the Shapley value by sampling, and the samples are mined — so attribution precision is bought with energy, exactly as the bound requires. it also means no protocol redesign can make decentralized attribution both sharp and cheap: a trustworthy division of credit has a thermodynamic price floor, and reusing the proof-of-work hash as the sample is the least wasteful way to pay it
the derived metric the network should report: attribution precision per joule
see landauer limit · fluctuation theorem · rewards · physical analogies
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