Configurational entropy of hard particles in a confined cavity

We study the configurational entropy S of N hard particles confined in a 2D cavity using MC integration, considering particles and cavities with various geometries. For small N, we find S decreases monotonically as the cavity aspect ratio increases regardless of particle shape. For large N, we find crystalline order within the cavity, with alternating regions of high and low particle density. We find the highest density near the boundary for all particle and cavity shape combinations, while the spatial distribution of the density changes with cavity shape. Our findings may give clues to engineering particles in a confined environment, entropic barriers, and systems with depletion interaction.