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Equation 4 · Part 3 · 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

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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