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Equation 2 · Part 4 · After Moore: The Adaptive Radiation of Compute

=

Emin⁡=kBTln⁡2E_{\min} = k_B T \ln 2
=

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

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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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

These citations provide research context; check each source for the exact claim it supports.