For systems of fused-hard-sphere molecules, we relate cavity distributions to free-volume distributions and derive new statistical geometry relations between thermodynamic and cavity properties.  From these results, we formulate two different approaches for calculating the pressure of systems of two-dimensional homonuclear hard dumbbells in terms of the geometry of the free volume of a molecule observed over the course of a simulation. We find excellent agreement between the pressure as calculated via both approaches and the pressure as calculated from simulations. We also calculate the distribution of free volumes in the solid phase. The nature of the distribution of free volumes changes abruptly near the hard-disk limit, similarly to the sudden change in validity of the fluctuating cell theory approximation in the previous paper.

• Contact: Jim Rainwater