Overdamped Langevin dynamics in a driven nonequilibrium steady state. Visualize trajectory distributions and the Hatano-Sasa excess entropy production.
1.00
0.50
1.50
20
—
Hatano-Sasa (2001)
ẋ = μ(−∂V/∂x + F) + √(2μT)·ξ
Excess entropy: σ_ex = −∂ₜln φ_ss along trajectory
HS identity: ⟨e^{−σ_ex}⟩ = 1
Generalizes Jarzynski to nonequilibrium steady states. Drive F tilts potential; particles accumulate on downhill side.
NESS: probability current J = φ_ss·(F − T∂ₓln φ_ss) ≠ 0.