Dissipar: Fluctuation Dissipation Theorem
Thermodynamics & Statistical Physics arc, page 66 of 193. Back to The Pixelated Physics Universe
Who they are
Dissipar has one line, and says it often: “How you fidget predicts how you respond.”
Dissipar 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
Fluctuation–dissipation theorem: the spectrum of equilibrium fluctuations determines the linear response (dissipation).
$$ \begin{gathered} \langle V^{2} \rangle = 4 k_B T R\, \Delta f \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\langle V^{2} \rangle$ | mean-square noise voltage | V^2 |
| $k_B$ | Boltzmann constant | J/K |
| $T$ | temperature | K |
| $R$ | resistance (dissipation) | Ω |
| $\Delta f$ | measurement bandwidth | Hz |
Sources
- H. B. Callen & T. A. Welton, Phys. Rev. 83, 34 (1951)
- R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
- H. Nyquist, Phys. Rev. 32, 110 (1928)
Crossovers
Dissipar meets Flukessa (Fluctuation Theorem Entropy). Dissipar reads a system's response from its equilibrium fluctuations. Flukessa's theorem extends that bookkeeping far from equilibrium. Near equilibrium, the two agree.
Dissipar meets Degreeda (Equipartition 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: Fluctuation Dissipation Theorem, Dissipar, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics