  We investigate cage breaking in dense hard disk systems using a model of
three Brownian disks confined within a circular corral. This system has a
six-dimensional configuration space, but can be equivalently thought to explore
a symmetric one-dimensional free energy landscape containing two energy minima
separated by an energy barrier. The exact free energy landscape can be
calculated as a function of system size. Results of simulations show the
average time between cage breaking events follows an Arrhenius scaling when the
energy barrier is large. We also discuss some of the consequences of using a
one-dimensional representation to understand dynamics in a multi-dimensional
space, such as diffusion acquiring spatial dependence and discontinuities in
spatial derivatives of free energy.
