Classical Langevin Equation

Available identifiers

same as (classical) Newton's equation of motion, but with additional terms for friction|damping and for stochastic collisions added

Note that a Langevin equation can be reformulated as a Fokker–Planck equation governing a probability distribution.

Defining Formula: $M \frac{d^{2}}{d t^{2}} \vec{q} = F (q) - γ \frac{d}{d t} q + \sqrt{2 γ k_{B} T} R (t)$
$F$ symbol represents Classical Force
$M$ symbol represents Mass
$R (t)$ symbol represents White Noise
$T$ symbol represents Temperature
$γ$ symbol represents Friction Coefficient
$k_{B}$ symbol represents Boltzmann Constant
$q$ symbol represents Classical Position
$t$ symbol represents Time

Lua error in Module:Formula at line 170: attempt to index local 'item' (a nil value).