Taulock: Critical Slowing Down
Thermodynamics & Statistical Physics arc, page 61 of 193. Back to The Pixelated Physics Universe
Who they are
Taulock has one line, and says it often: “Near the deadline, relaxation diverges.”
Taulock 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
Critical slowing down: near a critical point the relaxation time diverges, τ ∝ ξz.
$$ \begin{gathered} \tau \propto \xi^{z} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\tau$ | relaxation time | s |
| $\xi$ | correlation length | m |
| $z$ | dynamic critical exponent | — |
Sources
Crossovers
Taulock meets Avergail (Mean Field Theory). Avergail's mean field works away from the critical point. Taulock lives at it, where fluctuations grow across all scales and relaxation slows down without limit. That is exactly where mean-field theory fails.
Taulock meets Percolia (Percolation Threshold). Percolia's threshold is a critical point too. Near p_c the cluster sizes diverge, just as correlation lengths do near Taulock's critical temperature.
Wear the lore
- Taulock, the Critical-Point Sleeper Mug
- Related infographic poster: Critical Opalescence – Plate 015 Physics Poster
Concept keywords: Critical Slowing Down, Taulock, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics