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Equation 91 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol N_perp

N⊥[Γ]N_\perp[\Gamma]
N⊥N_\perp

What this part means

NpN_perp 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

NpN_perp 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

Everything above concerns N⊥N_\perp[Γ\Gamma] , a bound on unitary orthogonalizations, which cost no minimum heat in principle: a sequence of reversible gates can in principle run adiabatically, with no thermodynamic floor at all beyond the ordinary Levitin-Toffoli rate. Reading out a result, however, generally requires erasing or resetting some register, and that step is bound by a different and independent piece of physics, Landauer’s principle: erasing one bit at local temperature T costs at least kBk_BTln⁡\ln2 of dissipated heat [ 6 ] , made precise with finite-size corrections by Reeb and Wolf [ 7 ] . This bound does not care about horizons at all except through whatever value T takes locally —…

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