Symbol N_perp

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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$\leq$ 2$\pi$ $k_B$RE/($\hbar$ c) [ 8 ] . For a processor of size R=1\,$\mathrm{cm}$ holding E=1\,$\mathrm J$ of available energy, this gives S$\lesssim$27\,$\mathrm{J\,K^{-1}}$ , equivalent to roughly 2.9$\times$10^{24} bits of maximum distinguishable entropy — a static capacity ceiling, not a rate. Erasing that many bits at 10\,$\mathrm{mK}$ would cost at least $Q_{\min}$=ST$\approx$0.27\,$\mathrm J$ , more than a quarter of the entire energy budget assumed available, entirely independent of any horizon.…

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