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Equation 4 · Part 5 · After Moore: The Adaptive Radiation of Compute

subscript

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}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

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 →

Sources cited in the surrounding passage

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