Position histogram
Velocity distribution
Stats
Langevin equation: m·ẍ = −∂V/∂x − γ·ẋ + √(2γk_BT)·η(t), where η is Gaussian white noise.
Overdamped limit (γ→∞): ẋ = −(1/γ)·∂V/∂x + √(2k_BT/γ)·η.
At equilibrium, positions follow the Boltzmann distribution P(x) ∝ e^(−V(x)/k_BT).
Double-well barrier crossings (Kramers escape) increase exponentially with T.