- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Uniqueness of Landau-Lifshitz energy frame in relativistic dissipative hydrodynamics

Kyosuke Tsumura

Teiji Kunihiro

  • Analysis Technology Center, Fujifilm Corporation, Kanagawa 250-0193, Japan

  • Department of Physics, Kyoto University, Kyoto 606-8502, Japan

PDF

Phys. Rev. E 87, 053008 – Published 13 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.053008

Abstract

We show that the relativistic dissipative hydrodynamic equation derived from the relativistic Boltzmann equation by the renormalization-group method uniquely leads to the one in the energy frame proposed by Landau and Lifshitz, provided that the macroscopic-frame vector, which defines the local rest frame of the flow velocity, is independent of the momenta of constituent particles, as it should. We argue that the relativistic hydrodynamic equations for viscous fluids must be defined on the energy frame if consistent with the underlying relativistic kinetic equation.

View figure in article

Article Text

References (38)

  1. See the review articles P. Huovinen, in Quark Gluon Plasma 3, edited by R. C. Hwa and X. N. Wang (World Scientific, Singapore, 2003), p. 600; P. F. Kolb and U. W. Heinz, in Quark Gluon Plasma 3, edited by R. C. Hwa and X. N. Wang (World Scientific, Singapore, 2003), p. 634.
  2. M. Gyulassy and L. McLerran, Nucl. Phys. A 750, 30 (2005).
  3. P. Bozek, Acta Phys. Polon. B 43, 689 (2012).
  4. T. Hirano, P. Huovinen, K. Murase, and Y. Nara, Prog. Part. Nucl. Phys. 70, 108 (2013).
  5. For a review article, see, for example, D. Balsara, Astrophys. J. Suppl. 132, 83 (2001).
  6. J. C. Fabris, S. V. B. Goncalves and R. de Sa Ribeiro, Gen. Rel. Grav. 38, 495 (2006); R. Colistete, Jr., J. C. Fabris, J. Tossa, and W. Zimdahl, Phys. Rev. D 76, 103516 (2007).
  7. C. Eckart, Phys. Rev. 58, 919 (1940).
  8. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1959).
  9. P. Van and T. S. Biro, Phys. Lett. B 709, 106 (2012).
  10. T. Osada, Phys. Rev. C 85, 014906 (2012).
  11. W. A. Hiscock and L. Lindblom, Phys. Rev. D 31, 725 (1985); see also K. Tsumura and T. Kunihiro, Phys. Lett. B 668, 425 (2008); Y. Minami and T. Kunihiro, Prog. Theor. Phys. 122, 881 (2009); and Ref. [9].
  12. W. Israel, Ann. Phys. 100, 310 (1976).
  13. W. Israel and J. M. Stewart, Ann. Phys. 118, 341 (1979).
  14. S. R. de Groot, W. A. van Leeuwen and C. G. van Weert, Relativistic Kinetic Theory (Elsevier North-Holland, Amsterdam, 1980).
  15. C. Cercignani and G. M. Kremer, The Relativistic Boltzmann Equation (Birkhauser, Berlin, 2002).
  16. M. Dudynski and M. L. Ekiel-Jezewska, Phys. Rev. Lett. 55, 2831 (1985).
  17. R. M. Strain, Commun. Math. Phys. 300, 529 (2010).
  18. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1939).
  19. H. Grad, Comm. Pure Appl. Math. 2, 331 (1949).
  20. N. G. van Kampen, J. Stat. Phys. 46, 709 (1987).
  21. K. Tsumura, T. Kunihiro, and K. Ohnishi, Phys. Lett. B 646, 134 (2007).
  22. K. Tsumura and T. Kunihiro, Prog. Theor. Phys. 126, 761 (2011).
  23. L. Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 73, 1311 (1994); Phys. Rev. E 54, 376 (1996).
  24. T. Kunihiro, Prog. Theor. Phys. 94, 503 (1995); 95, 835(E) (1996); Jpn. J. Ind. Appl. Math. 14, 51 (1997); Prog. Theor. Phys. 97, 179 (1997).
  25. S.-I. Ei, K. Fujii, and T. Kunihiro, Ann. Phys. 280, 236 (2000).
  26. See for recent developments E. Kirkinis, Phys. Rev. E 77, 011105 (2008); H. Chiba, J. Math. Phys. 49, 102703 (2008); SIAM J. Appl. Dyn. Sys. 8, 1066 (2009); R. E. O’Malley, Jr, and E. Kirkinis, Stud. Appl. Math. 124, 383 (2010).
  27. K. Tsumura and T. Kunihiro, Eur. Phys. J. A 48, 162 (2012).
  28. K. Tsumura and T. Kunihiro, Prog. Theor. Phys. Suppl. 195, 19 (2012).
  29. F. Jüttner, Ann. Phys. 339, 856 (1911).
  30. J. Guckenheimer and P. Holmes, Nonlinear Oscillators, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, Berlin, 1983); J. D. Crawford, Rev. Mod. Phys. 63, 991 (1991); See also Y. Kuramoto, Prog. Theor. Phys. Suppl. 99, 244 (1989).
  31. Y. Hatta and T. Kunihiro, Ann. Phys. 298, 24 (2002):
  32. T. Kunihiro and K. Tsumura, J. Phys. A 39, 8089 (2006).
  33. I. Müller and T. Ruggeri, Rational Extended Thermodynamics (Springer-Verlag, Berlin, 1993).
  34. K. Ohnishi, K. Tsumura, and T. Kunihiro (to be published).
  35. K. Tsumura and T. Kunihiro (to be published); a preliminary report is given in Refs. [27,28].
  36. T. Dedeurwaerdere, J. Casas-Vazquez, D. Jou, and G. Lebon, Phys. Rev. E 53, 498 (1996).
  37. Y. Minami and Y. Hidaka, Phys. Rev. E 87, 023007 (2013).
  38. H. Mori, Prog. Theor. Phys. 33, 423 (1965).

Outline

Information

Phys. Rev. E 87, 053008– Published 13 May, 2013
  • Received 18 June 2012

©2013 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation