Figure 1: A 2D schematic of a configuration of particles with exclusion disks 
(left). The volume of the cavity that is formed upon removal of the central 
particle is the free volume v f of that particle (right). The interface of that 
cavity is the particle's free surface area s f . 
Figure 2: A typical 2D configuration of exclusion disks is shown with its 
corresponding Voronoi (solid lines) and Delaunay (dashed lines) tessellations. 
A set of Voronoi vertices connected by edges that lie entirely within the void 
region represents a cavity. 
Figure 3: Proof that upon removal of i, only geometric neighbors of i (i.e., 
k, but not j) must be re­tessellated. See text for discussion. 
Figure 4: A typical configuration of disks before the central particle is re­ 
moved (left). After the central particle is removed (right), the tessellation 
must be reconstructed inside of the superpolyhedron (bold, dashed­line). 
Thus, the volume and surface area of the cavity that once held atom i can 
be determined. 
Figure 5: The dimensionless pressure fiP=ae of the hard­sphere system as 
calculated from both free­volume information and the molecular dynamics 
(MD) collision rate. The Carnahan­Starling [56] equation is also shown for 
comparison. 
Figure 6: Free­volume distributions for densites ae \Lambda = 0.8, 0.85, 0.9, 0.91, 
0.93, 0.943 (freezing density), 0.95, and 0.96. The solid lines represent the 
fit to equation (12). 
Figure 7: The cavity­size distribution p of the hard­sphere fluid at density 
ae \Lambda = 0:8 as calculated from free­volume information and direct measurement. 
Figure 8: The cavity­size distribution p of the hard­sphere fluid at the freezing 
density ae \Lambda = 0:943 as calculated from free­volume information and direct 
measurement. 
Figure 9: The excess chemical potential ¯ ex is shown as calculated from 
the cavity­volume statistics. The excess chemical potential consistent with 
the Carnahan­Starling [56] and Sanchez [57] equations of state along with 
accurate data obtained by the methods of Attard [58] and Labik­Smith [59] 
are shown for comparison.