Molecular-dynamics verification of a final velocity distribution of a nonergodic system of hard parallel squares

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Abstract
The system of nonergodic hard parallel squares (HPS) appears to be the first nontrivial model for noncentral molecular interactions which seems to bypass the hydrodynamic stage in reaching a final non-Maxwellian velocity distribution. Nevertheless, HPS exhibit the molecular correlations not unlike those exhibited by more conventional ergodic systems. Here we present the initial and the final velocity distributions of Carlier and Frisch and compare the final numerical velocity distribution to an analytic expression obtained as the final stationary distribution from a Boltzmann equation for this system. We find agreement to within 5% for the computed and the calculated results. The Einstein diffusion coefficient and other transport coefficients are calculated for HPS and compared to the results for hard discs. We find that the final velocity distribution depends strongly on the initial distribution. We show that if initially a Maxwellian velocity distribution were selected, the distribution will remain Maxwellian.

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