which is equivalent to the improvement factor (IF) of Lundborg et al. when σ 2 (∆ F 0,1 ) is obtained with a uniform distribution of sampling time. We could have presented an equivalent discussion in terms of thermodynamic length. √ g λ σ ∂H ∂λ dλ, can be regarded as a measure of thermodynamic length which accounts for autocorrelation. If autocorrelation is ignored, g = 1 for all values of λ and the appropriate measure of thermodynamic length is 1 0 σ ∂H ∂λ dλ. However, the assumption of g = 1 means that minimising this length does not minimise overall uncertainty.