M d 2 d t 2 q → = F ( q ) − γ d d t q + 2 γ k B T R ( t )
R ( t )
k B
Note that a Langevin equation can be reformulated as a Fokker–Planck equation governing a probability distribution.
Classical Langevin Equation
same as (classical) Newton's equation of motion, but with additional terms for friction|damping and for stochastic collisions added