← Back to article

Equation 2 · After Moore: The Adaptive Radiation of Compute

What does this equation mean?

Emin⁡=kBTln⁡2E_{\min} = k_B T \ln 2

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsk_B T ln 2
Result or conditionE_min
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

Emin⁡E_{\min}

Symbol E_min

EmE_min is part of the quantity the equation computes from the expression on the right.

Understand this part →

kBk_B

Symbol k_B

kBk_B is an input to the expression that computes the quantity on the left.

Understand this part →

TT

Symbol T

the absolute temperature.

Understand this part →

=

=

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

Understand this part →

See an illustrated explanation →
subscript

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.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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…
Read the full surrounding passage
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: Emin⁡=kBTln⁡2E_{\min} = k_B T \ln 2. 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:

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to After Moore: The Adaptive Radiation of Compute

See this formula across 1 published context →

Browse the mathematical compendium →