  We present a simple model system with four hard disks moving in a circular
region for which free energy landscapes can be directly calculated and
visualized in two and three dimensions. We construct several energy landscapes
for our system and explore the strengths and limitations of each in terms of
understanding system dynamics, in particular the relationship between state
transitions and free energy barriers. We also demonstrate the importance of
distinguishing between system dynamics in real space and those in landscape
coordinates, and show that care must be taken to appropriately combine dynamics
with barrier properties to understand the transition rates. This simple model
provides an intuitive way to understand free energy landscapes, and illustrates
the benefits free energy landscapes can have over potential energy landscapes.
