These observations have consequences for the design of adaptive protocols. Because σ ∂H ∂λ converges quickly, minimum variance protocols can be found from short test simulations. These protocols are equivalent to minimum thermodynamic length protocols where the metric does not account for statistical inefficiency. Because √ t λ σ ∂H ∂λ λ converges slowly, minimum standard error of the mean protocols cannot easily be found from short simulations, and require adaptive protocols. These protocols are equivalent to minimum thermodynamic length protocols where the metric accounts for statistical inefficiency.