Abstract
It is shown that the pair correlation function (which is by definition the high-density factor in the revised Enskog theory) is not always a well-defined functional of the local density. Moreover, for a finite system with periodic boundary conditions and in the space homogeneous case, this function, computed at the contact value, is bounded at the maximum allowed density (i.e., a densityn max such that, in one dimension, 1/a−1/L⩽n max<1/a; equality sign, which corresponds to the usual close-packing density for whichL/a is an integer, being included as a particular case). At least for the one-dimensional gas model this finite value is shown to approach infinity in the thermodynamic and in the hydrodynamic limits. A new form for the revised Enskog equation, which does not depend on the inverse conjecture, is finally given.
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Cannone, M., Cercignani, C. The inverse conjecture for the revised Enskog equation. J Stat Phys 63, 363–387 (1991). https://doi.org/10.1007/BF01026610
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DOI: https://doi.org/10.1007/BF01026610