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The fluid and solid equations of state for hard parallel squares and cubesare reinvestigated here over a wide range of densities. We use a novelsingle-speed version of molecular dynamics. Our results are compared with thosefrom earlier simulations, as well as with the predictions of the virial series,the cell model, and Kirkwood's many-body single-occupancy model. Thesingle-occupancy model is applied to give the absolute entropy of the solidphases just as was done earlier for hard disks and hard spheres. The excellentagreement found here with all relevant previous work shows very clearly thatconfigurational properties, such as the equation of state, do not require themaximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squaresand hard cubes the free-volume theory provides a good description of thehigh-density solid-phase pressure. Hard parallel squares appear to exhibit asecond-order melting transition at a density of 0.79 relative to close-packing.Hard parallel cubes have a more complicated equation of state, with severalrelatively-gentle curvature changes, but nothing so abrupt as to indicate afirst-order melting transition. Because the number-dependence for the cubes isrelatively large the exact nature of the cube transition remains unknown.

Single-Speed Molecular Dynamics of Hard Parallel Squares and Cubes