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t∗  ∼  β2π ln⁡S,β≡ℏkBTH=8πGMc3t_* \;\sim\; \frac{\beta}{2\pi}\,\ln S, \qquad \beta \equiv \frac{\hbar}{k_BT_H} = \frac{8\pi GM}{c^3}

Why this formula appears here

The natural timescale for tLt_L is the scrambling time, and it is worth deriving in real units rather than only in the abstract. Sekino and Susskind conjectured that black holes are the fastest scramblers nature permits, mixing information across all their degrees of freedom in a time growing only logarithmically with entropy [ 2 ] . Maldacena, Shenker, and Stanford later proved the sharp version of the bound this conjecture leans on: the exponential growth rate of an out-of-time-order correlator, the operational signature of chaos, cannot exceed λL\lambda_L ≤\le 2π\pi/β\beta for a thermal system at inverse temperature β\beta , with a black hole horizon saturating the bound [ 3 ] . Combining a…

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kBk_B

Symbol k_B

kBk_B occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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THT_H

Symbol T_H

THT_H occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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c3c^3

Symbol c^3

c3c^3 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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t∗  ∼  β2π ln⁡S,β≡ℏkBTH=8πGMc3,t_* \;\sim\; \frac{\beta}{2\pi}\,\ln S, \qquad \beta \equiv \frac{\hbar}{k_BT_H} = \frac{8\pi GM}{c^3},

Equation 64 · Evolutionary Physics

The Bit Comes Back Before the Bearing

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The natural timescale for tLt_L is the scrambling time, and it is worth deriving in real units rather than only in the abstract. Sekino and Susskind conjectured that black holes are the fastest scramblers nature permits, mixing information across all their degrees of freedom in a time growing only logarithmically with entropy [ 2 ] . Maldacena, Shenker, and Stanford later proved the sharp version of the bound this conjecture leans on: the exponential growth rate of an out-of-time-order correlator, the operational signature of chaos, cannot exceed λL\lambda_L ≤\le 2π\pi/β\beta for a thermal system at inverse temperature β\beta , with a black hole horizon saturating the bound [ 3 ] . Combining a…

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