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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Cattaneo (editor), Relativistic Fluid Dynamics. Edizioni Cremonese, Rome 1971.
S. Chandrasekhar, Phys. Rev. Letters 24, 611 (1970).
J.L. Friedman and B.F. Schutz, Astrophys. J. 222, 281 (1978).
C. Cutler and L. Lindblom, Astrophys. J. 314, 234 (1987).
J.L. Friedman, J.R. Ipser and L. Parker, Astrophys. J. 304, 115 (1986).
L.L. Lindblom and W.A. Hiscock, Astrophys. J. 267, 384 (1983).
W.A. Hiscock and L. Lindblom, Ann. Physics 151, 466 (1983). See also their contribution to this volume.
C. Cattaneo, Compt. Rend. Acad. Sci. (Paris) 247, 431 (1958).
J.L. Synge, Relativity: The Special Theory. North-Holland, Amsterdam 1956.
W. Israel, Lettere al Nuovo Cimento 7, 860 (1973).
I. Bailey, Ann. Phys. 119, 76 (1979).
I. Bailey and W. Israel, Ann. Physics 130, 188 (1980).
M.M. Som, M.L. Bedran and E.P. Vasconcellos-Vaidya, Physics Letts. A117, 169 (1986).
V.H. Hamity, Phys. Rev. 187, 1745 (1969).
D. van Dantzig, Nederl. Akad. Wetensch. Proc. 42, 608 (1939).
O. Klein, Rev. Mod. Phys. 21, 531 (1949).
N.G. van Kampen, Phys. Rev. 173, 295 (1968).
W. Israel and J.M. Stewart, in General Relativity and Gravitation (ed. A. Held), Vol. 2, p. 491. Plenum, New York 1980.
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.
C.W. Bernard, Phys. Rev. D9, 3312 (1974).
K. Chou, Z. Su, B. Hao and L. Yu, Physics Reports 118, 1 (1985).
A.J. Niemi and G.W. Semenoff, Ann. Physics 152, 105 (1984).
E. Calzetta and B.L. Hu, Phys. Rev. D35, 495 (1987).
R.D. Jordan, Phys. Rev. D33, 444 (1986).
A.J. Niemi, Physics Letts. 203B, 425 (1988).
T. Arimitsu, M. Guida and H. Umezawa, Physica 148A, 1 (1988).
M. Ban and T. Arimitsu, Physica 146A, 89 (1987).
H. Matsumoto, Z. Physik C34, 335 (1987).
O. Eboli, R. Jackiw and S.-Y. Pi, Phys. Rev. D (in press, 1988).
L. van Hove, Physics Reports 137, 11 (1986).
N.P. Landsman and Ch.G. van Weert, Physics Reports 145, 141 (1987).
W.G. Dixon, Arch. Ration. Mech. Anal. 80, 159 (1982).
W. Israel, Physics Letts. 86A, 79 (1981).
W. Israel, J. Non-Equilib. Thermodyn. 11, 295 (1986).
T.L. Ho and N.D. Mermin, Phys. Rev. B21, 5190 (1980).
D.A. Kirzhnitz, Soviet Physics Uspekhi 9, 692 (1967).
M. Ichiyanagi, Progr. Theor. Phys. 66, 1 (1981).
T. Toyoda, Ann. Physics 141, 154 (1982).
M.A.B. Beg and R.C. Furlong, Phys. Rev. D31, 1370 (1985).
S. Coleman and E. Weinberg, Phys. Rev. D7, 1888 (1973).
A.B. Migdal, Rev. Mod. Phys. 50, 107 (1978).
H.E. Haber and H.A. Weldon, Phys. Rev. D25, 502 (1982).
J.I. Kapusta, Phys. Rev. D24, 426 (1981).
E.J. Kerrer, V. de la Incera and A.E. Shabad, Nuovo Cimento 98A, 245 (1987).
D. Pines and M.A. Alpar, Nature 316, 27 (1985).
G.E. Volovik, Soviet Physics Uspekhi 27, 363 (1984).
E.B. Sonin, Rev. Mod. Phys. 59, 87 (1987).
D.M. Sedrakyan, K.M. Shakhabasyan and A.G. Movsisyan, Astrofizika 19, 175 (1983).
J. Casas-Vásquez, D. Jou and G. Lebon (editors), Recent Developments in Nonequilibrium Thermodynamics. Springer Verlag, Berlin 1984.
I.-S. Liu, I. Müller and T. Ruggeri, Ann. Physics 169, 191 (1986).
C. Eckart, Phys. Rev. 58, 919 (1940).
L.D. Landau and E.M. Lifshitz, Fluid Mechanics, §127. Pergamon Press, London 1958.
N.G. van Kampen, J. Stat. Phys. 46, 709 (1987).
W.A. Hiscock and L. Lindblom, Phys. Rev. D31, 725 (1985).
C. Cattaneo, Sulla Conduzione del Calore. Atti del Seminario Matematico e Fisico della Universitá di Modena 3 (1948).
I. Müller, Zeitschr. f. Physik 198, 329 (1967).
J. Meixner, Ann. Physik 39, 333 (1941).
I. Prigogine, Physica 15, 272 (1949).
C.G. van Weert, Physica 111A, 537 (1982); Ann. Physics 149, 133 (1982).
M. Ekiel-Jezewska and L.A. Turski, Preprint, Institute for Theoretical Physics, Polish Academy of Sciences 1982; also ref. [34], p. 414.
E.I. Takizawa, Mem. Fac. Engng, Nagoya 5, 1 (1953).
J. Meixner, Zeitschr. f. Physik 139, 30 (1954).
C. Cercignani, Phys. Rev. Letters 50, 1122 (1983).
M. Dudyński and M.L. Ekiel-Jezewska, Phys. Rev. Letters 55, 2831 (1985).
E.g., H.G. Reik, Zeitschr. f. Physik 148, 156 (1957).
I. Müller, Zeitschr. f. Physik 198, 329 (1967).
W. Israel and J.M. Stewart, Ann. Physics 118, 341 (1979).
M.A. Schweizer, Astrophys. Journ. 258, 798 (1982).
D. Jou and D. Pavon, Astrophys. Journ. 291, 447 (1985).
V.A. Belinskii, E.J. Nikomarov and I.M. Khalatnikov, Soviet Physics JETP 50, 213 (1979).
H. Grad, Commun. Pure Appl. Math. 5, 257 (1952).
A.M. Anile and A. Majorana, Meccanica 16, 149 (1981).
A. Majorana and S. Motta, J. Non-Equilib. Thermodyn. 10, 1 (1985).
K.S. Thorne, Astrophys. J. 179, 897 (1973).
P.A. Koch, Phys. Rev. 140A, 1161 (1965).
G.F. Chapline and T.A. Weaver, Phys. Fluids 33, 1884 (1979).
A.M. Anile, J.C. Miller and S. Motta, Phys. Fluids 26, 1450 (1983).
M.I. Sobel, P.J. Siemens, J.P. Bondorf and H.A. Bethe, Nucl. Phys. A251, 502 (1975).
R.D. Blandford and C.F. McKee, Mon. Not. Roy. Astron. Soc. 180, 343 (1977).
D. Gilbarg, Amer. J. Math. 73, 256 (1951).
D. Gilbarg and D. Paolucci, Journ. Rat. Mech. Anal. 2, 617 (1953).
F.S. Sherman and L. Talbot, in Rarefied Gas Dynamics (ed. F.M. Devienne), p. 161. Academic Press, New York 1960.
K. Hansen and D.F. Hornig, Chem. Phys. 33, 913 (1960).
M.N. Kogan, Rarefied Gas Dynamics, p. 335. Plenum Press, New York 1969.
G.A. Bird, J. Fluid Mech. 30, 479 (1967).
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.
J. Serrin, Handbuch der Physik, Vol. 8, Pt. 1, p. 227. Springer, Berlin 1958.
S.R. de Groot, W.A. van Leeuwen and C.G. van Weert, Relativistic Kinetic Theory. North-Holland, Amsterdam 1980.
Author information
Authors and Affiliations
Editor information
Rights 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