Fokker-Planck Equation — Double Well Potential
Steady-state P(x)~e^{−V(x)/D} and Kramers escape rate over barrier
Fokker-Planck equation: ∂P/∂t = ∂/∂x[V'(x)P] + D ∂²P/∂x²
where V(x) = ax⁴ − 2x² + bx (double well with tilt b).
Steady state: P_ss(x) = Z⁻¹ e^{−V(x)/D} (Boltzmann with effective temperature D).
Kramers escape rate: r ≈ (ω_min ω_max)/(2π) · e^{−ΔV/D}
where ω²_min = |V''(x_min)|, ω²_max = |V''(x_max)| at barrier top.