Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · assumption · 39b16f67

Assumption: Semiclassical luminosity matching on a validity domain

Stage 3: energy, erasure cost, and a conditional mass law › The luminosity and clock are additional inputs · lines 1394–1416

Hawk04-D@1#ass:luminosity, Hawk04-D@1#eq:power

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On $M \in [M_{c}, M_{0}]$ , with $M_{c} > 0$ , a proposed model supplies a time normalization, outgoing flux observable, and power law

P (M) = α \sum \int_{0}^{\infty} \frac{d ω}{2 π} \frac{ω Γ _{α} ( M , ω )}{exp ( ω / T _{H} ( M )) - η _{α}} .

Here $η_{α} = 1$ for bosons and $- 1$ for fermions; degeneracies are included in $α$ . The integrals and sum are finite. For the cubic-scaling specialization, the species are massless and fixed, and

Γ_{α} (M, ω) = γ_{α} (M ω) .

The mass balance is additionally supplied as $M ˙ = - P (M)$ , or with a declared forcing error.

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Hawk04-D@1#eq:power · line 1399
$P (M) = α \sum \int_{0}^{\infty} \frac{d ω}{2 π} \frac{ω Γ _{α} ( M , ω )}{exp ( ω / T _{H} ( M )) - η _{α}} .$
unlabeled · line 1411
$Γ_{α} (M, ω) = γ_{α} (M ω) .$

Assumption: Semiclassical luminosity matching on a validity domain

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