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Prog. Theor. Phys. Vol. 25 No. 4 (1961) pp. 537-578

[ Full Text PDF : FREE ACCESS (3478K) ]

A New Approach to the Theory of Classical Fluids. III

— General Treatment of Classical Systems —

Tohru Morita and Kazuo Hiroike*

Research Institute for Fundamental Physics, Kyoto University, Kyoto
*Department of Physics, Tokyo Institute of Technology, Tokyo

(Received November 4, 1960)

Abstract:

A classical system enclosed in a finite volume and exerted by external forces is treated in quite a general way. The main results, which may be applicable to solids as well as to fluids, are as follows. Exact integral equations are found for the one- and two-particle distribution functions. Some thermodynamic functions are expressed in terms of these distribution functions. It is shown that there exist variational principles saying that the grand partition function is to be maximum with respect to the variations in the one- and two-particle distribution functions. Variational principles are found also for the Helmholtz free energy. It is suggested that Mayer's theory of condensation may in fact give the end point of the metastable gaseous state. It is pointed out that the hyper-netted chain approximation, proposed previously by one of the present auhors, has a meaning in solids as well as in fluids.


URL : http://ptp.ipap.jp/link?PTP/25/537/
DOI : 10.1143/PTP.25.537

[ Full Text PDF : FREE ACCESS (3478K) ] Citation:

References:

  1. T. Morita and K. Hiroike, Prog. Theor. Phys. 23 (1960), 1003[PTP].
  2. K. Hiroike, Prog. Theor. Phys. 24 (1960), 317[PTP].
  3. T. Morita and K. Hiroike, Prog. Theor. Phys. 24 (1960), 679[PTP].
  4. T. Morita, Prog. Theor. Phys. 23 (1960), 829[PTP].
  5. E. E. Salpeter, Ann. of Phys. 5 (1958), 183[CrossRef].
  6. See, for example, T. L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).
  7. K. Hiroike, J. Phys. Soc. Jpn. 12 (1957), 864[JPSJ].
  8. J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1940), Chapter 13.
  9. J. M. J. van Leeuwen, J. Groeneveld and J. de Boer, Physica 25 (1959), 792[CrossRef].
  10. E. Meeron, J. Math. Phys. 1 (1960), 192[CrossRef].
  11. C. N. Yang and T. D. Lee, Phys. Rev. 87 (1952), 404[APS].
  12. J. E. Mayer and M. G. Mayer, loc. cit., Chapter 14.
    J. E. Mayer, J. Chem. Phys. 19 (1951), 1024[CrossRef].
  13. S. Katsura and H. Fujita, J. Chem. Phys. 19 (1951), 795[CrossRef]; Prog. Theor. Phys. 6 (1951), 498[PTP].
  14. K. Ikeda, Proc. Int. Conf. Theor. Phys. Kyoto and Tokyo, (1953), 544; Prog. Theor. Phys. 16 (1956), 341[PTP].
  15. S. Katsura, J. Chem. Phys. 22 (1954), 1277[CrossRef]; Prog. Theor. Phys. 11 (1954), 476[PTP]; ibid. 13 (1955), 571[PTP].
  16. S. Katsura an H. Fujita, Prog. Theor. Phys. 5 (1950), 997[PTP].
  17. K. Ikeda, Prog. Theor. Phys. 11 (1954), 336[PTP]; ibid. 19 (1958), 653[PTP].
  18. T. Morita, Prog. Theor. Phys. 20 (1958), 920[PTP]; ibid. 21 (1959), 361 [PTP][Errata; 23 (1960), 843[PTP]].
  19. E. Meeron, Prog. Theor. Phys. 24 (1960), 588[PTP].
  20. A. E. Rodriguez. Proc. R. Soc. A 196 (1949), 73.
  21. K. Ikeda et al., a lecture at the meeting of the Physical Society of Japan held at Nagoya University on October 18, 1960.
    See also, K. Ikeda, Prog. Theor. Phys. 23 (1960), 616[PTP].
  22. S. Katsura and K. Harumi, Proc. Phys. Soc. 75 (1960), 826.
  23. G. S. Rushbrooke, Physica 26 (1960), 259[CrossRef].
  24. J. G. Kirkwood, V. A. Lewinson and B. J. Alder, J. Chem. Phys. 20 (1952), 929[CrossRef].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 62 (1993) pp. 170-178 :
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  2. Journal of the Physical Society of Japan 63 (1994) pp. 984-994 :
    Phase Diagram of the Nematic-Smectic A Transition of the Binary Mixture of Parallel Hard Cylinders of Different Lengths
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  3. Journal of the Physical Society of Japan 64 (1995) pp. 3787-3797 :
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    Tomonori Koda and Hatsuo Kimura
  4. Journal of the Physical Society of Japan 65 (1996) pp. 3551-3556 :
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  5. Progress of Theoretical Physics Vol. 27 No. 2 (1962) pp. 342-360 :
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  6. Progress of Theoretical Physics Vol. 27 No. 2 (1962) pp. 423-425 :
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  7. Progress of Theoretical Physics Vol. 27 No. 2 (1962) pp. 425-427 :
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  8. Progress of Theoretical Physics Vol. 27 No. 5 (1962) pp. 1025-1062 :
    Some Remarks on the Theory of Condensation
    Takesi Yosida and Kazuyosi Ikeda
  9. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 339-349 :
    An Interpolation of the HNC and PY Integral Equations for Classical Fluids
    Tohru Morita
  10. Progress of Theoretical Physics Vol. 52 No. 3 (1974) pp. 860-870 :
    Virial Theorem for the Jastrow-Type Ground State of a Bose Fluid
    Kazuo Hiroike
  11. Progress of Theoretical Physics Supplement No.115 (1994) pp. 69-81 :
    Application of the Cluster Variation Formalism to the Theory of Fluids
    A. G. Schlijper

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