Degreeda: Equipartition Theorem
Thermodynamics & Statistical Physics arc, page 50 of 193. Back to The Pixelated Physics Universe
Who they are
Degreeda has one line, and says it often: “½kt per degree of freedom. i have none left.”
Degreeda 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
Equipartition: ½kBT per quadratic degree of freedom; frozen modes at low T contribute nothing.
$$ \begin{gathered} \langle E \rangle = \tfrac{1}{2} k_B T \quad \text{per quadratic degree of freedom} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\langle E \rangle$ | mean energy | J |
| $k_B$ | Boltzmann constant | J/K |
| $T$ | temperature | K |
Sources
- L. Boltzmann, Wien. Ber. 63, 679 (1871)
- K. Huang, Statistical Mechanics (Wiley, 1987)
Crossovers
Degreeda meets Asymptor (Third Law of Thermodynamics). Degreeda gives ½k_BT to every active quadratic degree of freedom. Asymptor lowers the temperature until quantum level spacing freezes those modes out, one by one. Equipartition is a high-temperature rule.
Degreeda meets Dissipar (Fluctuation Dissipation Theorem). Degreeda sets the size of thermal jiggling: ½k_BT per mode. Dissipar links that jiggling to friction. The resistor's Johnson noise is one example where the two meet.
Wear the lore
Concept keywords: Equipartition Theorem, Degreeda, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics