Fluctuation Theorem & Jarzynski Equality

PF(W) / PR(−W) = exp(W/kT)  |  ⟨e−W/kT⟩ = e−ΔF/kT

⟨W⟩F —
ΔF (Jarzynski) —
ΔF (exact) —
Jarzynski error —
Blue: PF(W) forward
Red: PR(−W) reverse
Particle dragged in harmonic well
V(x,t) = ½k(x−vt)²
Langevin dynamics, Δt=0.01
Bottom: log ratio = W/kT test