Journal of Statistical Physics

, Volume 36, Issue 3–4, pp 471–488 | Cite as

On the validity of the inverse conjecture in classical density functional theory

  • J. T. Chayes
  • L. Chayes


It is shown that the basic assumptions of the classical density functional approach are rigorously correct forH-stable systems in the grand canonical ensemble. Moreover, it is established that the set of all single-particle densities is convex. These results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single-particle densities. Analogous results are obtained for the solution of the higher-order correlation inverse problem, and the ramifications of these results for the validity of two-body decomposition of forces are discussed.

Key words

Inverse problem density functional theory V-representability two-body decomposition 


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  1. 1.
    J. T. Chayes, L. Chayes, and E. H. Lieb,Commun. Math. Phys. 93:57 (1984).Google Scholar
  2. 2.
    F. H. Stillinger and F. P. Buff,J. Chem. Phys. 37:1 (1962).Google Scholar
  3. 3.
    J. L. Lebowitz and J. K. Percus,J. Math. Phys. 4:116 (1963).Google Scholar
  4. 4.
    R. Evans,Adv. Phys. 28, 143 (1979).Google Scholar
  5. 5.
    A. Robledo and C. Varea,J. Stat. Phys. 26:513 (1981).Google Scholar
  6. 6.
    J. K. Percus, inThe Liquid State of Matter, Studies in Statistical Mechanics, Vol. VIII, E. W. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1982), p. 31.Google Scholar
  7. 7.
    J. K. Percus,J. Stat. Phys. 15:505 (1976).Google Scholar
  8. 8.
    J. K. Percus,J. Stat. Phys. 28:67 (1982).Google Scholar
  9. 9.
    E. H. Lieb, inPhysics as Natural Philosophy: Essays in Honor of Laszlo Tisza on His 75th Birthday, A. Shimony and H. Feshbach, eds. (M.I.T. Press, Cambridge, 1982), p. 111.Google Scholar
  10. 10.
    J. T. Chayes, thesis, Princeton University, 1983.Google Scholar
  11. 11.
    J. D. Weeks, private communication.Google Scholar
  12. 12.
    M. Yamada,Progr. Theor. Phys. 25:579 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • J. T. Chayes
    • 1
  • L. Chayes
    • 1
  1. 1.Department of PhysicsPrinceton UniversityPrinceton

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