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R=1 cmR=1\,\mathrm{cm}

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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≤\leq 2π\pi kBk_BRE/(ℏ\hbar c) [ 8 ] . For a processor of size R=1\,cm\mathrm{cm} holding E=1\,J\mathrm J of available energy, this gives S≲\lesssim27\,J K−1\mathrm{J\,K^{-1}} , equivalent to roughly 2.9×\times10^{24} bits of maximum distinguishable entropy — a static capacity ceiling, not a rate. Erasing that many bits at 10\,mK\mathrm{mK} would cost at least Qmin⁡Q_{\min}=ST≈\approx0.27\,J\mathrm J , more than a quarter of the entire energy budget assumed available, entirely independent of any horizon.…

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R=1 cmR=1\,\mathrm{cm}

Equation 98 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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≤\leq 2π\pi kBk_BRE/(ℏ\hbar c) [ 8 ] . For a processor of size R=1\,cm\mathrm{cm} holding E=1\,J\mathrm J of available energy, this gives S≲\lesssim27\,J K−1\mathrm{J\,K^{-1}} , equivalent to roughly 2.9×\times10^{24} bits of maximum distinguishable entropy — a static capacity ceiling, not a rate. Erasing that many bits at 10\,mK\mathrm{mK} would cost at least Qmin⁡Q_{\min}=ST≈\approx0.27\,J\mathrm J , more than a quarter of the entire energy budget assumed available, entirely independent of any horizon.…

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