Langevin Dynamics

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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.