Free energy landscapes for a small number of hard disks

We present our analysis on the free energy landscapes for a small number (N < 10) of simulated particles undergoing a 2-dimensional random walks inside of a circular corral. For each value of N certain preferred configurations exist where the system will spend most of its time. We identify these equilibrium configurations and monitor for transitions between them. For a transition to occur, collective motion must concentrate enough free space to allow one particle to move in-between two others. This allows us to define the state of the system as the smallest displacement needed for one particle to make such a passing. Thus, we are able to reduce the dimensionality of the configuration from 2N to 1 and we can describe a free energy landscape in this single dimension. The heights of the free energy barriers between equilibrium states and the time between transitions increase with power law scaling as the amount of free space in the corral is reduced. We seek to understand how this scaling changes as we increase the number of particles in the system. We hope that by understanding how re-arrangements occur for these small systems, we will help illuminate how the dynamics of larger, glassy systems arise.