• Erasa Landauer Limit pixel-art physics T-shirt, white tee, front view

IndexHeat & EntropyTee

Erasa

Forgetting Costs Heat Physics

\[\langle Q \rangle \ge k_B T \ln 2\]
$29.99 USD
$29.99 USD
Sale Sold out
Size
Color

Size guide S–5XL · inches

Erasa wipes a bit clean and a puff of heat drifts off. Forgetting is never free.

The Physics

Erasing one bit of information, resetting a memory to a standard state no matter what it held, must on average release at least k_B T ln 2 of heat into the surroundings. At 300 K that is 2.87 × 10⁻²¹ J, about 0.018 eV. The cost comes from erasure; it does not apply to every logical step.

⟨Q⟩ ≥ k_B T ln 2

  • Q: heat released per erased bit (J)
  • k_B: Boltzmann constant, 1.380649 × 10⁻²³ J/K
  • T: temperature (K)
  • ln 2: ≈ 0.693 (dimensionless)

Rolf Landauer proposed it in 1961, and Bérut et al. measured it with a single trapped colloidal bead (Nature, 2012).

Honest caveat: It applies to logically irreversible erasure, not to every computation.

On the shirt

Front: Erasa, the pixel-art character, with the title. Back: the Landauer bound, its value at 300 K and the 1961 and 2012 sources. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

For scale: size M is 20 in (50.80 cm) wide, about 3.143 × 1034 Planck lengths (lP = 1.616255 × 10−35 m). A tape measure is quicker.

Measurements in inches, ±1.5 in tolerance.

ShippingBy destination

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

I wipe a bit clean, and a little puff of heat drifts off. Forgetting is never free.

Erasing a bit means resetting a memory to a standard state no matter what it held: two possible inputs, one output. Rolf Landauer argued in 1961 that this logically irreversible step must, on average, release at least k_B T ln 2 of heat into the surroundings. At 300 K that is about 2.87 × 10⁻²¹ joules, roughly 0.018 eV.

In 2012 Bérut and colleagues erased a bit stored in a single glass bead held in a double-well laser trap; as the erasure slowed down, the average heat approached the Landauer bound. It is a lower bound on the average, so single runs can come in below it, and it applies to erasure, not to every computation.

Equations

\[\langle Q \rangle \ge k_B T \ln 2\]
\[T = 300\ \mathrm{K}: \quad k_B T \ln 2 \approx 2.87\times10^{-21}\ \mathrm{J} \approx 0.018\ \mathrm{eV}\]
SymbolMeaningUnit
\(Q\) heat released to the surroundings per erased bit \(\mathrm{J}\)
\(k_B\) Boltzmann constant, 1.380 649 × 10⁻²³ J/K (exact) \(\mathrm{J/K}\)
\(T\) temperature of the surroundings \(\mathrm{K}\)
\(\ln 2\) natural log of 2 ≈ 0.693 \(\mathrm{1}\)

Sources

  1. Landauer (1961) Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev. 5, 183
  2. Bérut et al. (2012) Experimental verification of Landauer's principle linking information and thermodynamics, Nature 483, 187
  3. NIST CODATA: Boltzmann constant

Field notes

View all
1 3
View all