Shapes within shapes: how particles arrange inside a cavity

We calculate the configurational entropy of hard particles confined in a cavity using Monte Carlo integration. Multiple combinations of particle and cavity shapes are considered. For small numbers of particles $N$, we show that the entropy decreases monotonically with increasing cavity aspect ratio, regardless of particle shape. As $N$ increases, we find ordered regions of high and low particle density, with the highest density near the boundary for all particle and cavity shape combinations. Our findings provide insights relevant to engineering particles in confined spaces, entropic barriers, and systems with depletion interactions.