Langevin Dynamics

Stochastic differential equation: m ẍ = -∇V(x) - γẋ + √(2γkT) η(t). Particles explore energy landscapes driven by thermal noise vs restoring forces.

mẍ = −∇V − γẋ + ξ(t)
⟨ξ(t)ξ(t')⟩ = 2γkT δ(t−t')
Boltzmann: P ∝ e^{−V/kT}