Equation 4 · After Moore: The Adaptive Radiation of Compute
What does this equation mean?
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This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol k_B
is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
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.
superscript
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.
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What the article says around this equation
where 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: . 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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where 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: . 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 single-bit scale [ 2 ] . The bound is real, it has been measured, and every irreversible logic technology — which is to say every lineage covered in this article except the one this section is actually about — has to dissipate at least that much heat every time it erases a bit, no matter how exotic its switching mechanism is.
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