  Rare transitions between long-lived stable states are often analyzed in terms
of free energy landscapes computed as functions of a few collective variables.
Here, using transitions between geometric phases as example, we demonstrate
that the effective dynamics of a system along these variables are an essential
ingredient in the description of rare events and that the static perspective
provided by the free energy alone may be misleading. In particular, we
investigate the disk-to-slab transition in the two-dimensional Ising model
starting with a calculation of a two-dimensional free energy landscape and the
distribution of committor probabilities. While at first sight it appears that
the committor is incompatible with the free energy, they can be reconciled with
each other using a two-dimensional Smoluchowski equation that combines the free
energy landscape with state dependent diffusion coefficients. These results
illustrate that dynamical information is not only required to calculate rate
constants but that neglecting dynamics may also lead to an inaccurate
understanding of the mechanism of a given process.
