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Equation 97 · Part 6 · A Horizon Is a Toll Booth, Not a Loophole

Symbol c

S≤2πkBRE/(ℏc)S\leq 2\pi k_BRE/(\hbar c)
cc

What this part means

c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…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…

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