Skip to main content
SpringerLink
Log in

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

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. T. Chayes, L. Chayes, and E. H. Lieb,Commun. Math. Phys. 93:57 (1984).

    Google Scholar 

  2. F. H. Stillinger and F. P. Buff,J. Chem. Phys. 37:1 (1962).

    Google Scholar 

  3. J. L. Lebowitz and J. K. Percus,J. Math. Phys. 4:116 (1963).

    Google Scholar 

  4. R. Evans,Adv. Phys. 28, 143 (1979).

    Google Scholar 

  5. A. Robledo and C. Varea,J. Stat. Phys. 26:513 (1981).

    Google Scholar 

  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. J. K. Percus,J. Stat. Phys. 15:505 (1976).

    Google Scholar 

  8. J. K. Percus,J. Stat. Phys. 28:67 (1982).

    Google Scholar 

  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. J. T. Chayes, thesis, Princeton University, 1983.

  11. J. D. Weeks, private communication.

  12. M. Yamada,Progr. Theor. Phys. 25:579 (1961).

    Google Scholar 

Download references

Author information

Author notes

  1. J. T. Chayes & L. Chayes

    Present address: Department of Physics, Harvard University, 02138, Cambridge, Massachusetts

Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, New Jersey

    J. T. Chayes & L. Chayes

Authors
  1. J. T. Chayes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Chayes
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by the National Science Foundation under grants PHY-8116101 A01 (J.T.C.), PHY-8301493 (L.C.) and PHY-8203669 (J.T.C. and L.C.).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chayes, J.T., Chayes, L. On the validity of the inverse conjecture in classical density functional theory. J Stat Phys 36, 471–488 (1984). https://doi.org/10.1007/BF01010992

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01010992

Key words

Search

Navigation