We generated λ-schedules using thermodynamic speeds of 0.5, 1.0, 2.0, and 4.0 kcal mol -1 (Equation ). The cost of the protocol was negligible, but it generated more consistent off-diagonal overlap values than the manually-optimised schedule (Figure ). This was especially true for the vanish stages, where the thermodynamic length varied least linearly as a function of λ. Figure ) shows λ against the the normalised λ index ( Index No.windows ), where a steeper curve of of λ against the normalised index indicates a lower density of windows. Here, the adaptive protocols reduces the density of states close to λ = 1, avoiding the increase in overlap observed for the non-adaptive protocol in this region (Figure ).