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Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids

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Abstract

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics.

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References

  1. J. P. Boon and S. Yip, Molecular Hydrodynamics, McGraw-Hill, New York (1980).

    Google Scholar 

  2. R. D. Mountain, Adv. Mol. Relax. Proc., 9, 225 (1977).

    Article  Google Scholar 

  3. S. W. Lovesey and T. Springer, Dynamics of Solids and Liquids by Neutron Scattering (Topics Current Phys., Vol. 3), Springer, Berlin (1977).

    Google Scholar 

  4. P. Resibois and M. De Leneer, Classical Kinetic Theory of Fluids, Wiley, New York (1977).

    Google Scholar 

  5. L. P. Kadanoff and P. C. Martin, Ann. Phys., 24, 419 (1963).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. M. V. Sergeev, Theor. Math. Phys., 21, 1234 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  7. S. V. Tischenko, Theor. Math. Phys., 26, 62 (1976).

    Article  Google Scholar 

  8. I. M. de Schepper, E. G. D. Cohen, C. Bruin, J. C. van Rijs, W. Montrooij, and L. A. de Graaf, Phys. Rev. A, 38, 271 (1988).

    Article  ADS  Google Scholar 

  9. Yu. A. Tserkovnikov, Theor. Math. Phys., 63, 619 (1985).

    Article  MathSciNet  Google Scholar 

  10. I. M. Mryglod and M. V. Tokarchuk, “On statistical hydrodynamics of simple fluids: Generalized transport coefficients [in Russian],” Preprint IFKS 91-6U, URSR Academy of Sciences, Kiev (1991).

    Google Scholar 

  11. I. M. Mryglod and M. V. Tokarchuk, Prob. Atomic Sci. Technol., No. 3(24), 134 (1992).

  12. I. M. Mryglod, I. P. Omelyan, and M. V. Tokarchuk, Mol. Phys., 84, 235 (1995).

    Article  ADS  Google Scholar 

  13. D. N. Zubarev, Nonequilibruim Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York (1974).

    Google Scholar 

  14. D. N. Zubarev, “Modern methods of the statistical theory of nonequilibrium processes [in Russian],” in: Itogi Nauki i Tekhniki: Sovr. Prob. Mat., Vol. 15, VINITI, Moscow (1980), p. 131.

    Google Scholar 

  15. D. Zubarev, V. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes, Vol. 2, Relaxation and Hydrodynamic Processes, Akademie, Berlin (1997).

    Google Scholar 

  16. D. N. Zubarev and M. V. Tokarchuk, Theor. Math. Phys., 70, 164 (1987).

    Article  Google Scholar 

  17. A. Z. Akcasu and E. Deniels, Phys. Rev. A, 2, 962 (1970).

    Article  ADS  Google Scholar 

  18. I. M. Mryglod, “Statistical theory of collective excitations in fluids: Approach of collective generalized modes [in Ukrainian],” Author’s review of doctoral dissertation, Ivan Franko Lviv Natl. Univ., Lvov (2000).

    Google Scholar 

  19. I. P. Omelyan and I. M. Mryglod, Cond. Matter Phys., No. 4, 128 (1994).

  20. I. M. Mryglod and I. P. Omelyan, Phys. Lett. A, 205, 401 (1995).

    Article  ADS  Google Scholar 

  21. I. M. Mryglod, M. V. Tokarchuk, and R. Folk, Phys. A, 220, 325 (1995).

    Article  Google Scholar 

  22. I. M. Mryglod and R. Folk, Phys. A, 234, 129 (1996).

    Article  Google Scholar 

  23. I. M. Mryglod and M. V. Tokarchuk, Theor. Math. Phys., 115, 479 (1998).

    Article  MATH  Google Scholar 

  24. I. M. Mryglod, Yu. K. Rudavskii, M. V. Tokarchuk, and O. F. Batsevych, Ukrainian J. Phys., 44, 1030 (1999).

    Google Scholar 

  25. I. M. Mryglod, Yu. K. Rudavskii, M. V. Tokarchuk, and O. F. Batsevych, Ukrainian J. Phys., 44, 1174 (1999).

    Google Scholar 

  26. I. Mryglod, R. Folk, S. Dubyk, and Yu. Rudavskii, Cond. Matter Phys., 2, No. 2(18), 221 (1999).

    Google Scholar 

  27. I. P. Omelyan, I. M. Mryglod, and M. V. Tokarchuk, Cond. Matter Phys., 1, No. 1(13), 179 (1998).

    Google Scholar 

  28. I. P. Omelyan, I. M. Mryglod, and M. V. Tokarchuk, Phys. Rev. E, 57, 6667 (1998).

    Article  Google Scholar 

  29. I. P. Omelyan, R. I. Gelem, and M. V. Tokarchuk, Ukrainian J. Phys., 42, 684 (1997).

    Google Scholar 

  30. I. P. Omelyn, Mol. Phys., 93, No. 1, 123 (1998).

    Article  Google Scholar 

  31. I. P. Omelyan and M. V. Tokarchuk, J. Phys. Cond. Matter, 12, L505 (2000).

    Article  Google Scholar 

  32. I. P. Omelyan, I. M. Mryglod, and M. V. Tokarchuk, Cond. Matter Phys., 8, No. 1(41), 25 (2005).

    Google Scholar 

  33. T. Bryk and I. Mryglod, J. Phys. Cond. Matter, 16, L463 (2004).

    Article  ADS  Google Scholar 

  34. T. Bryk and I. Mryglod, Cond. Matter Phys., 6, No. 3(35), 395 (2003).

    Google Scholar 

  35. T. Bryk and I. Mryglod, Phys. Rev. B, 71, 132202 (2005).

    Article  ADS  Google Scholar 

  36. V. V. Ignatyuk, I. M. Mryglod, and M. V. Tokarchuk, Fiz. Nizk. Temp., 25, 407 (1999).

    Google Scholar 

  37. V. V. Ignatyuk, I. M. Mryglod, and M. V. Tokarchuk, Fiz. Nizk. Temp., 25, 1145 (1999).

    Google Scholar 

  38. I. M. Mryglod, Cond. Matter Phys., No. 10, 115 (1997).

  39. T. M. Bryk, I. M. Mryglod, and G. Kahl, Phys. Rev. E, 56, 2903 (1997).

    Article  ADS  Google Scholar 

  40. T. M. Bryk and I. M. Mryglod, Phys. Lett. A, 261, 349 (1999).

    Article  ADS  Google Scholar 

  41. T. M. Bryk and I. M. Mryglod, Cond. Matter Phys., 2, No. 2(18), 285 (1999).

    Google Scholar 

  42. T. Bryk and I. Mryglod, Cond. Matter Phys., 7, No. 2(38), 285 (2004).

    Google Scholar 

  43. T. Bryk and I. Mryglod, J. Phys. Cond. Matter, 13, 1343 (2001).

    Article  ADS  Google Scholar 

  44. T. Bryk and I. Mryglod, J. Phys. Studies, 8, No. 1, 35 (2004).

    ADS  Google Scholar 

  45. T. Scopigno, U. Balucani, G. Ruocco, and F. Sette, Phys. Rev. E, 63, 011210 (2000).

    Google Scholar 

  46. A. V. Mokshin, R. M. Yulmetyev, R. M. Khusnutdinoff, and P. Hänggi, J. Phys. Cond. Matter, 19, 046209 (2007).

    Google Scholar 

  47. D. N. Zubarev, V. G. Morozov, I. P. Omelyan, and M. V. Tokarchuk, Theor. Math. Phys., 87, 412 (1991).

    Article  MathSciNet  Google Scholar 

  48. D. N. Zubarev, V. G. Morozov, I. P. Omelyan, and M. V. Tokarchuk, Theor. Math. Phys., 96, 997 (1993).

    Article  MathSciNet  Google Scholar 

  49. M. V. Tokarchuk, I. P. Omelyan, and A. E. Kobryn, Cond. Matter Phys., 1, No. 4(16), 687 (1998).

    Google Scholar 

  50. V. G. Morozov, A. E. Kobryn, and M. V. Tokarchuk, Cond. Matter Phys., No. 4, 117 (1994).

  51. I. P. Omelyan and M. V. Tokarchuk, Phys. A, 234, 89 (1996).

    Article  Google Scholar 

  52. A. E. Kobryn, I. P. Omelyan, and M. V. Tokarchuk, J. Stat. Phys., 92, 973 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  53. A. E. Kobryn, V. G. Morozov, I. P. Omelyan, and M. V. Tokarchuk, Phys. A, 230, 189 (1996).

    Article  Google Scholar 

  54. P. A. Hlushak and M. V. Tokarchuk, Cond. Matter Phys., 7, No. 3(39), 639 (2004).

    Google Scholar 

  55. I. M. Mryglod and V. V. Ignatyuk, J. Phys. Studies, 1, No. 2, 181 (1997).

    MATH  ADS  Google Scholar 

  56. Yu. A. Tserkovnikov, Theor. Math. Phys., 85, 1096 (1990).

    Article  Google Scholar 

  57. Yu. A. Tserkovnikov, Theor. Math. Phys., 118, 85 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  58. Yu. A. Tserkovnikov, Theor. Math. Phys., 119, 511 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  59. I. M. Mryglod and A. M. Hachkevych, Cond. Matter Phys., No. 5, 105 (1995).

  60. G. O. Balabanyan, Theor. Math. Phys., 82, 317 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  61. G. O. Balabanyan, Theor. Math. Phys., 85, 1081 (1990).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lvov, Ukraine

    B. B. Markiv, I. P. Omelyan & M. V. Tokarchuk

Authors
  1. B. B. Markiv
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  2. I. P. Omelyan
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  3. M. V. Tokarchuk
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Correspondence to B. B. Markiv.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 91–101, January, 2008.

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Markiv, B.B., Omelyan, I.P. & Tokarchuk, M.V. Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids. Theor Math Phys 154, 75–84 (2008). https://doi.org/10.1007/s11232-008-0007-x

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