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Energy Accounts Sticker Sheet

Sortex, Invertia, Vevette & Moderon | 9 Pixel Art s

\[\begin{gathered} Q_{\text{erase}} \ge k_B T \ln 2 \end{gathered}\]
$19.99 USD
$19.99 USD
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The Energy Accounts sticker sheet gathers several Pixelated Physics characters on one page, each built on a real piece of physics. Nine kiss-cut pixel-art stickers on one A5 sheet: Sortex (Landauer), Invertia (negative temperature), Vevette (Higgs), Moderon (neutrons), plus props. Peel them off one at a time and stick them wherever the physics belongs.

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Details

What you getA5 sheet · 9 stickers

One A5 kiss-cut sheet (5.83″ × 8.27″) on white sticker paper with 9 stickers, made to order.

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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.

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The physics

Stickers about energy accounting: Landauer's minimum heat to erase a bit, negative absolute temperature, the Higgs field potential that gives particles mass, and the moderation of fast neutrons by collisions.

Nine stickers on one sheet: four characters who keep the books on energy, heat and mass.

Sortex’s line is Sorting Can Be Free. Forgetting Isn’t. Maxwell’s demon sorts fast molecules from slow ones. Rolf Landauer argued in 1961 that erasing one bit of memory must release at least k_BT ln 2 of heat, and Charles Bennett used this in 1982 to say that the demon pays when it resets its memory. The bound has been measured; whether it is the full exorcism is still argued. That is the chip turning an unknown bit, ?, into 0 and venting heat.

Invertia’s line is Top Floor First. Heat Only Leaves Me. A system with a highest energy level can hold more particles at the top than at the bottom. In the standard Boltzmann definition, that population has negative absolute temperature and is hotter than any positive temperature, so heat flows out of it into anything ordinary. Edward Purcell and Robert Pound made one with nuclear spins in 1951. Whether Boltzmann or Gibbs entropy is the right definition is still debated. That is the full upper level and the near-empty lower one, marked HOT.

Vevette’s line is Nothing at Zero. I Sit at 246. The Higgs potential has its minimum not at zero field but on a ring, so the vacuum carries a field value v ≈ 246 GeV, and particles get mass from their coupling to it. That is the ball resting in the rim of the potential, marked 246 GeV.

Moderon’s line is Same Mass. You Stop. I Roll. A neutron loses the most energy hitting something of its own mass. A head-on hit on a hydrogen nucleus, a proton, can take all of it, which is why water slows neutrons so well. Enrico Fermi’s group in Rome found the slow-neutron effect in 1934. That is the neutron and the proton of nearly equal mass, n ≈ p.

Equations

\[\begin{gathered} Q_{\text{erase}} \ge k_B T \ln 2 \end{gathered}\]
\[\begin{gathered} \frac{1}{T} = \frac{\partial S}{\partial E} < 0 \end{gathered}\]
\[\begin{gathered} V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4 \\ \begin{gathered} \langle\phi\rangle = \frac{v}{\sqrt{2}} \\ v = (\sqrt{2}\,G_F)^{-1/2} \end{gathered} \\ v \approx 246\ \text{GeV} \end{gathered}\]
\[\begin{gathered} \alpha = \left(\frac{A-1}{A+1}\right)^2 \end{gathered}\]
SymbolMeaningUnit
\(Q_{\text{erase}}\) heat released to the surroundings when one bit of memory is erased (a lower bound, not a fixed cost) \(\mathrm{J}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) absolute temperature: of the surroundings that absorb the erasure heat (first line); of the spin system, in the standard Boltzmann definition (second line) \(\mathrm{K}\)
\(\ln 2\) natural logarithm of 2: one bit is a choice between two states \(\mathrm{1}\)
\(S\) entropy (Boltzmann form, from the number of states at energy E) \(\mathrm{J/K}\)
\(E\) total energy of the spin system \(\mathrm{J}\)
\(V\) Higgs potential (energy density; natural units) \(\mathrm{GeV^4}\)
\(\phi\) Higgs field; on the art the horizontal axis is the field's size (natural units) \(\mathrm{GeV}\)
\(\mu^2\) parameter of the potential, positive \(\mathrm{GeV^2}\)
\(\lambda\) self-coupling of the field, positive \(\mathrm{1}\)
\(\langle\phi\rangle\) vacuum expectation value: where the field settles, in the valley \(\mathrm{GeV}\)
\(v\) electroweak scale, about 246.22 GeV \(\mathrm{GeV}\)
\(G_F\) Fermi coupling constant \(\mathrm{GeV^{-2}}\)
\(\alpha\) smallest possible ratio of neutron energy after to before one collision (a head-on hit) \(\mathrm{1}\)
\(A\) mass of the target nucleus in neutron masses (hydrogen: 1) \(\mathrm{1}\)

Sources

  1. Encyclopaedia Britannica — Maxwell’s demon
  2. Landauer (1961) Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev. 5, 183
  3. Purcell & Pound (1951) A Nuclear Spin System at Negative Temperature, Phys. Rev. 81, 279 (reversed state decayed with the 5-min time constant)
  4. Ramsey (1956) Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures, Phys. Rev. 103, 20
  5. Higgs (1964) Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13, 508
  6. Englert & Brout (1964) Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev. Lett. 13, 321
  7. Amaldi, D’Agostino, Fermi, Pontecorvo, Rasetti & Segrè (1935) Artificial radioactivity produced by neutron bombardment — II, Proc. R. Soc. A 149, 522–558
  8. NobelPrize.org — The Nobel Prize in Physics 1938 (Enrico Fermi; nuclear reactions brought about by slow neutrons)

Source Landauer, R. (1961). Irreversibility and Heat Generation in the Computing Process. IBM Journal of Research and Development 5, 183–191.doi.org/10.1147/rd.53.0183

Field notes

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