Erasa: Forgetting Costs Heat
Thermodynamics & Statistical Physics arc, page 46 of 193. Back to The Pixelated Physics Universe
Who they are
Erasa wipes a bit clean and a puff of heat drifts off. Forgetting is never free.
Erasa is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
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.
$$ \begin{gathered} \langle Q \rangle \ge k_B T \ln 2 \\ T = 300\ \mathrm{K}: \quad k_B T \ln 2 \approx 2.87\times10^{-21}\ \mathrm{J} \approx 0.018\ \mathrm{eV} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $Q$ | heat released to the surroundings per erased bit | J |
| $k_B$ | Boltzmann constant, 1.380 649 × 10⁻²³ J/K (exact) | J/K |
| $T$ | temperature of the surroundings | K |
| $\ln 2$ | natural log of 2 ≈ 0.693 | 1 |
Honest caveat: It applies to logically irreversible erasure, not to every computation.
Sources
- Landauer (1961) Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev. 5, 183
- Bérut et al. (2012) Experimental verification of Landauer's principle linking information and thermodynamics, Nature 483, 187
- NIST CODATA: Boltzmann constant
Crossovers
Erasa meets Bounda (Bekenstein Bound). Erasa says erasing a bit costs heat. Bounda says a region can only store a limited number of bits. Together they tie information to physics at both ends: storage and deletion.
Erasa meets Reversa (Loschmidt's Reversal Paradox). Reversa can flip every velocity, but Erasa reminds her that resetting a memory costs at least k_B T ln 2 of heat per bit. Undoing the record of what happened isn't free, so Reversa can't run the world backwards without paying the second law.
Erasa meets Jarza (Jarzynski Equality). Erasa's bound is an average. Jarza's equality says that individual runs can beat it, with work below the free-energy change, but the exponential average of e^(−W/k_BT) comes out exactly e^(−ΔF/k_BT).
Wear the lore
Concept keywords: Forgetting Costs Heat, Erasa, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics