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Equation 4 · Part 6 · After Moore: The Adaptive Radiation of Compute

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kBTln⁡2=(1.380649×10−23 JK)(300 K)(0.6931)≈2.87×10−21 J≈2.9 zJk_B T \ln 2 = \left(1.380649\times10^{-23}\ \tfrac{\text{J}}{\text{K}}\right)(300\ \text{K})(0.6931) \approx 2.87\times10^{-21}\ \text{J} \approx 2.9\ \text{zJ}
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

where kBk_B is Boltzmann’s constant. At room temperature — 300 kelvin, a reasonable stand-in for a chip’s operating temperature — plugging in Boltzmann’s constant’s exact SI value gives: kBTln⁡2=(1.380649×10−23 JK)(300 K)(0.6931)≈2.87×10−21 J≈2.9 zJk_B T \ln 2 = \left(1.380649\times10^{-23}\ \tfrac{\text{J}}{\text{K}}\right)(300\ \text{K})(0.6931) \approx 2.87\times10^{-21}\ \text{J} \approx 2.9\ \text{zJ}. That bound is not a rough estimate awaiting refinement; it has been directly tested. A 2012 experiment reported in Nature, using a colloidal silica bead trapped in an optical potential rather than an electronic circuit, measured the heat dissipated while erasing one bit of information stored in the bead’s position and found it consistent with the Landauer bound within experimental uncertainty in the low-erasure-rate limit, the first experiment to test the bound this directly at the…

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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