Skip to main content

Covariant fluid mechanics and thermodynamics: An introduction

  • Main Lectures
  • Conference paper
  • First Online:
Relativistic Fluid Dynamics

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1385))

Abstract

These lectures are intended as a pedagogical introduction to the covariant formulation of nonequilibrium and statistical thermodynamics and kinetic theory. The various formulations of nonequilibrium thermodynamics and their individual difficulties — with causality, stability, shock structure — are critically reviewed. As an illustration of the general formalism, a fairly detailed treatment is presented of the covariant statistical thermodynamics of superfluids.

Lectures delivered at C.I.M.E. Session on “Relativistic Fluid Dynamics” (ed. A.M. Anile and Y. Choquet-Bruhat) at Centro Studi Noto, Noto (Syracuse) May 25 – June 3, 1987

Work supported by Canadian Institute for Advanced Research and by Natural Sciences and Engineering Research Council of Canada

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Cattaneo (editor), Relativistic Fluid Dynamics. Edizioni Cremonese, Rome 1971.

    MATH  Google Scholar 

  2. S. Chandrasekhar, Phys. Rev. Letters 24, 611 (1970).

    Article  ADS  Google Scholar 

  3. J.L. Friedman and B.F. Schutz, Astrophys. J. 222, 281 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  4. C. Cutler and L. Lindblom, Astrophys. J. 314, 234 (1987).

    Article  ADS  Google Scholar 

  5. J.L. Friedman, J.R. Ipser and L. Parker, Astrophys. J. 304, 115 (1986).

    Article  ADS  Google Scholar 

  6. L.L. Lindblom and W.A. Hiscock, Astrophys. J. 267, 384 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  7. W.A. Hiscock and L. Lindblom, Ann. Physics 151, 466 (1983). See also their contribution to this volume.

    Article  ADS  MathSciNet  Google Scholar 

  8. C. Cattaneo, Compt. Rend. Acad. Sci. (Paris) 247, 431 (1958).

    MathSciNet  Google Scholar 

  9. J.L. Synge, Relativity: The Special Theory. North-Holland, Amsterdam 1956.

    MATH  Google Scholar 

  10. W. Israel, Lettere al Nuovo Cimento 7, 860 (1973).

    Article  Google Scholar 

  11. I. Bailey, Ann. Phys. 119, 76 (1979).

    Article  ADS  Google Scholar 

  12. I. Bailey and W. Israel, Ann. Physics 130, 188 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  13. M.M. Som, M.L. Bedran and E.P. Vasconcellos-Vaidya, Physics Letts. A117, 169 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  14. V.H. Hamity, Phys. Rev. 187, 1745 (1969).

    Article  ADS  Google Scholar 

  15. D. van Dantzig, Nederl. Akad. Wetensch. Proc. 42, 608 (1939).

    MathSciNet  Google Scholar 

  16. O. Klein, Rev. Mod. Phys. 21, 531 (1949).

    Article  ADS  Google Scholar 

  17. N.G. van Kampen, Phys. Rev. 173, 295 (1968).

    Article  ADS  Google Scholar 

  18. W. Israel and J.M. Stewart, in General Relativity and Gravitation (ed. A. Held), Vol. 2, p. 491. Plenum, New York 1980.

    Google Scholar 

  19. W. Israel, in Proceedings of the Third Moscow Seminar on Quantum Gravity (ed. M.A. Markov, V.A. Berezin and V.P. Frolov), p. 265. World Scientific, Singapore 1985.

    Google Scholar 

  20. C.W. Bernard, Phys. Rev. D9, 3312 (1974).

    ADS  Google Scholar 

  21. K. Chou, Z. Su, B. Hao and L. Yu, Physics Reports 118, 1 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  22. A.J. Niemi and G.W. Semenoff, Ann. Physics 152, 105 (1984).

    Article  ADS  Google Scholar 

  23. E. Calzetta and B.L. Hu, Phys. Rev. D35, 495 (1987).

    ADS  MathSciNet  Google Scholar 

  24. R.D. Jordan, Phys. Rev. D33, 444 (1986).

    ADS  Google Scholar 

  25. A.J. Niemi, Physics Letts. 203B, 425 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  26. T. Arimitsu, M. Guida and H. Umezawa, Physica 148A, 1 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  27. M. Ban and T. Arimitsu, Physica 146A, 89 (1987).

    Article  ADS  Google Scholar 

  28. H. Matsumoto, Z. Physik C34, 335 (1987).

    ADS  Google Scholar 

  29. O. Eboli, R. Jackiw and S.-Y. Pi, Phys. Rev. D (in press, 1988).

    Google Scholar 

  30. L. van Hove, Physics Reports 137, 11 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  31. N.P. Landsman and Ch.G. van Weert, Physics Reports 145, 141 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  32. W.G. Dixon, Arch. Ration. Mech. Anal. 80, 159 (1982).

    Article  Google Scholar 

  33. W. Israel, Physics Letts. 86A, 79 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  34. W. Israel, J. Non-Equilib. Thermodyn. 11, 295 (1986).

    Article  ADS  Google Scholar 

  35. T.L. Ho and N.D. Mermin, Phys. Rev. B21, 5190 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  36. D.A. Kirzhnitz, Soviet Physics Uspekhi 9, 692 (1967).

    Article  ADS  Google Scholar 

  37. M. Ichiyanagi, Progr. Theor. Phys. 66, 1 (1981).

    Article  ADS  Google Scholar 

  38. T. Toyoda, Ann. Physics 141, 154 (1982).

    Article  ADS  Google Scholar 

  39. M.A.B. Beg and R.C. Furlong, Phys. Rev. D31, 1370 (1985).

    ADS  Google Scholar 

  40. S. Coleman and E. Weinberg, Phys. Rev. D7, 1888 (1973).

    ADS  Google Scholar 

  41. A.B. Migdal, Rev. Mod. Phys. 50, 107 (1978).

    Article  ADS  Google Scholar 

  42. H.E. Haber and H.A. Weldon, Phys. Rev. D25, 502 (1982).

    ADS  Google Scholar 

  43. J.I. Kapusta, Phys. Rev. D24, 426 (1981).

    ADS  Google Scholar 

  44. E.J. Kerrer, V. de la Incera and A.E. Shabad, Nuovo Cimento 98A, 245 (1987).

    ADS  Google Scholar 

  45. D. Pines and M.A. Alpar, Nature 316, 27 (1985).

    Article  ADS  Google Scholar 

  46. G.E. Volovik, Soviet Physics Uspekhi 27, 363 (1984).

    Article  ADS  Google Scholar 

  47. E.B. Sonin, Rev. Mod. Phys. 59, 87 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  48. D.M. Sedrakyan, K.M. Shakhabasyan and A.G. Movsisyan, Astrofizika 19, 175 (1983).

    ADS  Google Scholar 

  49. J. Casas-Vásquez, D. Jou and G. Lebon (editors), Recent Developments in Nonequilibrium Thermodynamics. Springer Verlag, Berlin 1984.

    Google Scholar 

  50. I.-S. Liu, I. Müller and T. Ruggeri, Ann. Physics 169, 191 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  51. C. Eckart, Phys. Rev. 58, 919 (1940).

    Article  ADS  Google Scholar 

  52. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, §127. Pergamon Press, London 1958.

    MATH  Google Scholar 

  53. N.G. van Kampen, J. Stat. Phys. 46, 709 (1987).

    Article  ADS  Google Scholar 

  54. W.A. Hiscock and L. Lindblom, Phys. Rev. D31, 725 (1985).

    ADS  MathSciNet  Google Scholar 

  55. C. Cattaneo, Sulla Conduzione del Calore. Atti del Seminario Matematico e Fisico della Universitá di Modena 3 (1948).

    Google Scholar 

  56. I. Müller, Zeitschr. f. Physik 198, 329 (1967).

    Article  ADS  Google Scholar 

  57. J. Meixner, Ann. Physik 39, 333 (1941).

    Article  ADS  Google Scholar 

  58. I. Prigogine, Physica 15, 272 (1949).

    Article  ADS  MathSciNet  Google Scholar 

  59. C.G. van Weert, Physica 111A, 537 (1982); Ann. Physics 149, 133 (1982).

    Article  ADS  Google Scholar 

  60. M. Ekiel-Jezewska and L.A. Turski, Preprint, Institute for Theoretical Physics, Polish Academy of Sciences 1982; also ref. [34], p. 414.

    Google Scholar 

  61. E.I. Takizawa, Mem. Fac. Engng, Nagoya 5, 1 (1953).

    MathSciNet  Google Scholar 

  62. J. Meixner, Zeitschr. f. Physik 139, 30 (1954).

    Article  ADS  MathSciNet  Google Scholar 

  63. C. Cercignani, Phys. Rev. Letters 50, 1122 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  64. M. Dudyński and M.L. Ekiel-Jezewska, Phys. Rev. Letters 55, 2831 (1985).

    Article  ADS  Google Scholar 

  65. E.g., H.G. Reik, Zeitschr. f. Physik 148, 156 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  66. I. Müller, Zeitschr. f. Physik 198, 329 (1967).

    Article  ADS  Google Scholar 

  67. W. Israel and J.M. Stewart, Ann. Physics 118, 341 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  68. M.A. Schweizer, Astrophys. Journ. 258, 798 (1982).

    Article  ADS  Google Scholar 

  69. D. Jou and D. Pavon, Astrophys. Journ. 291, 447 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  70. V.A. Belinskii, E.J. Nikomarov and I.M. Khalatnikov, Soviet Physics JETP 50, 213 (1979).

    ADS  Google Scholar 

  71. H. Grad, Commun. Pure Appl. Math. 5, 257 (1952).

    Article  MathSciNet  Google Scholar 

  72. A.M. Anile and A. Majorana, Meccanica 16, 149 (1981).

    Article  ADS  Google Scholar 

  73. A. Majorana and S. Motta, J. Non-Equilib. Thermodyn. 10, 1 (1985).

    Article  Google Scholar 

  74. K.S. Thorne, Astrophys. J. 179, 897 (1973).

    Article  ADS  Google Scholar 

  75. P.A. Koch, Phys. Rev. 140A, 1161 (1965).

    Article  ADS  Google Scholar 

  76. G.F. Chapline and T.A. Weaver, Phys. Fluids 33, 1884 (1979).

    Article  ADS  Google Scholar 

  77. A.M. Anile, J.C. Miller and S. Motta, Phys. Fluids 26, 1450 (1983).

    Article  ADS  Google Scholar 

  78. M.I. Sobel, P.J. Siemens, J.P. Bondorf and H.A. Bethe, Nucl. Phys. A251, 502 (1975).

    Article  ADS  Google Scholar 

  79. R.D. Blandford and C.F. McKee, Mon. Not. Roy. Astron. Soc. 180, 343 (1977).

    Article  ADS  Google Scholar 

  80. D. Gilbarg, Amer. J. Math. 73, 256 (1951).

    Article  MathSciNet  Google Scholar 

  81. D. Gilbarg and D. Paolucci, Journ. Rat. Mech. Anal. 2, 617 (1953).

    MathSciNet  Google Scholar 

  82. F.S. Sherman and L. Talbot, in Rarefied Gas Dynamics (ed. F.M. Devienne), p. 161. Academic Press, New York 1960.

    Google Scholar 

  83. K. Hansen and D.F. Hornig, Chem. Phys. 33, 913 (1960).

    ADS  Google Scholar 

  84. M.N. Kogan, Rarefied Gas Dynamics, p. 335. Plenum Press, New York 1969.

    Book  Google Scholar 

  85. G.A. Bird, J. Fluid Mech. 30, 479 (1967).

    Article  ADS  Google Scholar 

  86. Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Vol. 2, p. 476. Academic Press, New York 1967.

    Google Scholar 

  87. J. Serrin, Handbuch der Physik, Vol. 8, Pt. 1, p. 227. Springer, Berlin 1958.

    Google Scholar 

  88. S.R. de Groot, W.A. van Leeuwen and C.G. van Weert, Relativistic Kinetic Theory. North-Holland, Amsterdam 1980.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Angelo M. Anile Yvonne Choquet-Bruhat

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Israel, W. (1989). Covariant fluid mechanics and thermodynamics: An introduction. In: Anile, A.M., Choquet-Bruhat, Y. (eds) Relativistic Fluid Dynamics. Lecture Notes in Mathematics, vol 1385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084030

Download citation

  • DOI: https://doi.org/10.1007/BFb0084030

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51466-4

  • Online ISBN: 978-3-540-48142-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics