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Equation 97 · Part 4 · A Horizon Is a Toll Booth, Not a Loophole

Symbol R

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

What this part means

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

Its job in the formula

R 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

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…

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