Equation 2 · After Moore: The Adaptive Radiation of Compute
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Symbol E_min
in is part of the quantity the equation computes from the expression on the right.
Symbol k_B
is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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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.
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Every lineage discussed so far competes on how close it can get to doing more with less energy per operation. There is a hard floor beneath all of them, derived not from engineering but from statistical mechanics, and it is worth stating precisely because the rest of this section depends on it. In 1961, the IBM physicist Rolf Landauer showed that any logically irreversible operation — one that destroys information, such as erasing a bit or overwriting one value with another without retaining a way to reconstruct the original — must dissipate a minimum amount of heat into its environment, because the entropy the erased information represented has to go somewhere, and the second law of…
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Every lineage discussed so far competes on how close it can get to doing more with less energy per operation. There is a hard floor beneath all of them, derived not from engineering but from statistical mechanics, and it is worth stating precisely because the rest of this section depends on it. In 1961, the IBM physicist Rolf Landauer showed that any logically irreversible operation — one that destroys information, such as erasing a bit or overwriting one value with another without retaining a way to reconstruct the original — must dissipate a minimum amount of heat into its environment, because the entropy the erased information represented has to go somewhere, and the second law of thermodynamics says it can only go up [ 1 ] . The minimum energy that erasing one bit must dissipate, at absolute temperature T , is: . 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:
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