Nonlinear transformations of the Muller potential. **a)** In the original coordinate system the simulations are run with diffusion constant *D*=1 and *k*_{B}T=9. The MRP in magenta and the drift path in blue are in close agreement. **b)** After the nonlinear transformation indicated by the axis labels, the diffusion tensor is now position dependent. Dashed lines are transformed paths, and solid lines are paths calculated in the new coordinates. Here the new drift path (solid dark blue) aligns with the original path (dashed blue) because the shift factor in is zero. The new MFEP path calculated for a string following the gradient at *k*_{B}T=9, shown for comparison in solid red, does not follow the reactive flux. **c)** For the nonlinear transformation indicated by the axis labels, the shift factor is not zero. As a result, the new drift path (solid dark blue) will not align exactly with the original drift path (dashed blue), but the effect of the shift is small relative to the magnitude of the original drift vector, and therefore the paths still closely align. The transformed original MRP is shown in dashed magenta. The magnitude of the flux has not changed significantly and both paths still appear to pass through the regions of highest flux.

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