Jarzynski
Equality
⟨e^{−βW}⟩ = e^{−βΔF} — free energy from non-equilibrium trajectories
Temperature β⁻¹ = kT
1.00
Pulling speed v
1.0
Protocol steps
50
N trajectories
100
Run Pulling Experiment
Work Distribution P(W)
—
⟨W⟩
—
−kT ln⟨e^{−βW}⟩
—
ΔF (true)
—
|error|
Jarzynski Convergence vs Sample Size
The Jarzynski estimator is dominated by rare low-work trajectories. Direct average ⟨W⟩ ≥ ΔF (second law). Exponential average converges to ΔF.