Equation 64 · Part 5 · The Bit Comes Back Before the Bearing

Symbol k_B

t_* \;\sim\; \frac{\beta}{2\pi}\,\ln S, \qquad \beta \equiv \frac{\hbar}{k_BT_H} = \frac{8\pi GM}{c^3},

k_B

What this part means

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

Its job in the formula

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

Full expressionSymbol k_BArticle meaning

The passage around this formula

The natural timescale for $t_L$ 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 $\lambda_L$ $\le$ 2 $\pi$ / $\beta$ for a thermal system at inverse temperature $\beta$ , with a black hole horizon saturating the bound [ 3 ] . Combining a…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.