  We calculate the configurational entropy of colloidal particles in a confined
geometry interacting as hard disks using Monte Carlo integration method. In
particular, we consider systems with three kinds of boundary conditions: hard,
periodic and spherical. For small to moderate packing fraction $\phi$ values,
we find the entropies per particle for systems with the periodic and spherical
boundary conditions tend to reach a same value with the increase of the
particle number $N$, while that for the system with the hard boundary
conditions still has obvious differences compared to them within the studied
$N$ range. Surprisingly, despite the small system sizes, the estimated
entropies per particle at infinite system size from extrapolations in the
periodic and spherical systems are in reasonable agreement with that calculated
using thermodynamic integration method. Besides, as $N$ increases we find the
pair correlation function begins to exhibit similar features as that of a large
self-assembled system at the same packing fraction. Our findings may contribute
to a better understanding of how the configurational entropy changes with the
system size and the influence of boundary conditions, and provide insights
relevant to engineering particles in confined spaces.
