Crooks Fluctuation Theorem

P_F(W) / P_R(−W) = e^{(W−ΔF)/kT} — forward and reverse work distributions cross at W = ΔF
1.00
2.0
300
60

Forward P_F(W) and Reverse P_R(−W) Distributions

ΔF (Crooks)
ΔF (Jarzynski)
0.00
ΔF (true)

Log Ratio ln[P_F(W)/P_R(−W)] vs W

Crooks: ln[P_F(W)/P_R(−W)] = β(W − ΔF)
Slope = β = 1/kT; x-intercept = ΔF

Crossing point of P_F and P_R gives ΔF directly.