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Equation 15 · Part 5 · A Horizon Is a Toll Booth, Not a Loophole

Symbol t

N≤2πℏ(⟨H⟩−E0)tN \leq \frac{2}{\pi\hbar}\left(\langle H\rangle-E_0\right) t
tt

What this part means

t 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

t 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

…that for a periodic evolution this rate integrates cleanly: a system with mean energy ⟨\langle H⟩\rangle-E0E_0 above its ground state can pass through at most N≤2πℏ(⟨H⟩−E0)tN \leq \frac{2}{\pi\hbar}\left(\langle H\rangle-E_0\right) t. mutually orthogonal states in elapsed time t [ 3 ] . Lloyd used the same bound to price computation itself: no amount of clever engineering lets a system with energy E execute logical operations faster than about 2E/π\piℏ\hbar per second, a ceiling with nothing to do with any particular hardware [ 5 ] .

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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