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Boltzmann-Enskog limit for equilibrium states of systems of hard spheres in the framework of a canonical ensemble

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Abstract

We prove the existence of the Boltzmann-Enskog limit for an equilibrium system of hard spheres. On the basis of analysis of the Kirkwood-Salsburg equations, we show that the limit distribution functions are constants that can be represented as series in density.

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References

  1. D. Ya. Petrina and K. D. Petrina, “On the existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit,” Dokl. Akad. Nauk Ukr., 2, 30–34 (1996).

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  2. D. Ya. Petrina and K. D. Petrina, “On the existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit,” Ukr. Mat. Zh., 49, No. 1, 112–121 (1997).

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  3. M. Lampis and D. Ya. Petrina, “The Boltzmann-Grad limit for equilibrium states of systems of hard spheres in the framework of canonical ensemble,” Math. Phys., Analysis, Geometry, No. 1-2, 112–132 (1997).

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  4. D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems, Gordon and Breach (1989).

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Authors and Affiliations

  1. Dipartimento di Matematica del Politecnico di Milano, Italia

    M. Lampis

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    D. Ya. Petrina

Authors
  1. M. Lampis
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  2. D. Ya. Petrina
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Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1195–1205, September, 1997.

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Lampis, M., Petrina, D.Y. Boltzmann-Enskog limit for equilibrium states of systems of hard spheres in the framework of a canonical ensemble. Ukr Math J 49, 1345–1356 (1997). https://doi.org/10.1007/BF02487342

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  • DOI: https://doi.org/10.1007/BF02487342

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