Title: Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system
Author(s):

V. M. Pergamenshchik (Institute of Physics of the National Academy of Sciences of Ukraine, avenu Nauki 46, Kyiv 03039, Ukraine; Center for Theoretical Physics of the Polish Academy of Sciences, al. Lotników 32/46, 02-668, Warsaw, Poland (current address))

The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory incorporates both contributions, and their sum is shown to determine the free volume and partition function. The approach is based on multiple intersections of the circles concentric with the disks but of twice larger radius. The result is exact formulae for the extensive and intensive entropy contributions in terms of the intersections of just two, three, four, and five circles. The method has an important advantage for applications in numerical simulations: the formulae enable one to convert the disk coordinates into the entropy contribution directly without any additional geometric construction. The theory can be straightforwardly applied to a system of hard spheres.

Key words: hard discs, free volume, partition function, intersections

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