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10mK
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[ 11 ] . Setting Tloc equal to a demanding but realistic dilution-refrigerator base temperature of 10\,mK and solving for the required clearance gives Δ r≈2.8×10^{-14}\,m — a few nuclear radii from the horizon. For a supermassive hole, in other words, the ambient Hawking bath stays colder than any laboratory cryostat until the processor is closer to the horizon than an atomic nucleus, twenty-odd orders of magnitude closer than the point at which the support-acceleration bill already becomes unpayable. Cooling is a genuine, non-negotiable line item — it is what ties this construction to horizon thermodynamics at all — but for this mass scale it is not…
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Equation 75 · Evolutionary Physics
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
[ 11 ] . Setting Tloc equal to a demanding but realistic dilution-refrigerator base temperature of 10\,mK and solving for the required clearance gives Δ r≈2.8×10^{-14}\,m — a few nuclear radii from the horizon. For a supermassive hole, in other words, the ambient Hawking bath stays colder than any laboratory cryostat until the processor is closer to the horizon than an atomic nucleus, twenty-odd orders of magnitude closer than the point at which the support-acceleration bill already becomes unpayable. Cooling is a genuine, non-negotiable line item — it is what ties this construction to horizon thermodynamics at all — but for this mass scale it is not…
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Article →Equation 102 · Evolutionary Physics
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
A second, independent ceiling bounds not the rate of erasure but the total information a bounded system can hold at all: the Bekenstein bound limits the entropy of a system of effective size R and energy E to S≤ 2π kBRE/(ℏ c) [ 8 ] . For a processor of size R=1\,cm holding E=1\,J of available energy, this gives S≲27\,JK−1 , equivalent to roughly 2.9×10^{24} bits of maximum distinguishable entropy — a static capacity ceiling, not a rate. Erasing that many bits at 10\,mK would cost at least Qmin=ST≈0.27\,J , more than a quarter of the entire energy budget assumed available, entirely independent of any horizon.…
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