Barrierwyn: Kramers Escape Rate
Thermodynamics & Statistical Physics arc, page 62 of 193. Back to The Pixelated Physics Universe
Who they are
Barrierwyn has one line, and says it often: “Escape rate: exponentially suppressed.”
Barrierwyn 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
Kramers escape: thermally activated rate over a barrier ΔE scales as e−ΔE/kBT.
$$ \begin{gathered} k \propto e^{-\Delta E / k_B T} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $k$ | escape rate | s^{-1} |
| $\Delta E$ | barrier height | J |
| $k_B$ | Boltzmann constant | J/K |
| $T$ | temperature | K |
Sources
Crossovers
Barrierwyn meets Vitressa (Glass Transition). Vitressa's glass is a liquid whose particles must hop over barriers to rearrange. As it cools, Barrierwyn's escape rate drops so steeply that the rearranging stops on any lab timescale.
Barrierwyn meets Kinessa (8 nm per Step). Kinessa's steps are biased by ATP, but thermal kicks are always around. Barrierwyn's escape over a barrier is part of how molecular motors move between states.
Barrierwyn meets Foldara (Levinthal's Paradox). Foldara's protein slides down a funnel instead of searching every shape. Barrierwyn's barriers along the way set how fast folding happens.
Wear the lore
Concept keywords: Kramers Escape Rate, Barrierwyn, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics