Information-theoretical approach to radiative transfer

Physica A: Statistical Mechanics and its Applications

Volumn 243, Issue 3-4, 1997, Pages 275-303

  Fort, J ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ENTROPY; FUNCTIONS; THERMAL DIFFUSION;

MAXIMUM ENTROPY FORMALISM; RADIAL DISTRIBUTION FUNCTION;

HEAT RADIATION;

EID: 0031234782     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(97)00277-X     Document Type: Article

References (77)

1. M. Planck, The Theory of Heat Radiation, Dover, New York, 1959.
2. L.D. Landau, E.M. Lifshitz, Statistical Physics, part 1, Pergamon, Oxford, 1980.
3. B. Callies, F. Herbert, J. Appl. Math. Phys. 39 (1988) 242.
4. m is dimensionless): see [2], Section 38.
5. S.R. DeGroot, P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York, 1984.
6. D. Jou, J. Casas-Vázquez, G. Lebon, Extended Irreversible Thermodynamics, Springer, Berlin, 1996.
7. S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge University Press, Cambridge, 1970.
8. H. Grad, Principles of the kinetic theory of gases, in: S. Flügge (Ed.), Handbuch der Physik XII. Springer, Berlin, 1958.
9. B.C. Eu, Kinetic Theory and Irreversible Thermodynamics, Wiley, New York, 1992.
10. E.T. Jaynes, Phys. Rev. 106 (1957) 620; 108 (1957) 171; E.T. Jaynes, in: R.D. Rosenkrantz (Ed.), Papers on Probability, Statistics and Statistical Physics, Reidel, Dordrecht, 1983.
11. E.T. Jaynes, Phys. Rev. 106 (1957) 620; 108 (1957) 171; E.T. Jaynes, in: R.D. Rosenkrantz (Ed.), Papers on Probability, Statistics and Statistical Physics, Reidel, Dordrecht, 1983.
12. E.T. Jaynes, Phys. Rev. 106 (1957) 620; 108 (1957) 171; E.T. Jaynes, in: R.D. Rosenkrantz (Ed.), Papers on Probability, Statistics and Statistical Physics, Reidel, Dordrecht, 1983.
13. M.N. Kogan, On the principle of maximum entropy, in: C.L. Brundin (Ed.), Rarified Gas Dynamics, Academic Press, New York, 1967.
14. F. Schlögl, Phys. Rep. 62 (1980) 267.
15. C. Tsallis, F.C. Sa Barreto, E.D. Loh, Phys. Rev. E 52 (1995) 1447.
16. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
17. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
18. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
19. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
20. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
21. C. Tsallis, J. Stat. Phys. 52 (1988) 479; E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; 24 (1991) 3187; 25 (1992) 1019; C. Tsallis, Phys. Lett. A 206 (1995) 389; C. Tsallis, D.J. Burkman, Phys. Rev. E 54 (1996) R2197.
22. I. Müller, T. Ruggeri, Extended Thermodynamics, Springer, Berlin, 1992.
23. M. Ferrer, D. Jou, Am. J. Phys. 63 (1995) 237.
24. L.S. García-Colín, A.R. Vasconcellos, R. Luzzi, J. Non-Equilib. Thermodyn. 19 (1994) 24.
25. For a brief and very clear comparison between Grad's method and information theory, see Ref. [6], p. 146. A detailed comparison including Enskog's method can be found in Ref. [11].
26. S. Harris, An Introduction to the Theory of the Boltzmann Equation, ch. 12, Holt, Rinehart and Winston, New York, 1971.
27. G.N. Minerbo, J. Quant. Spectrosc. Radiat. Transfer 20 (1978) 541.
28. See, e.g., K. Huang, Statistical Mechanics, Section 4.3, Wiley, New York, 1987.
29. P.S. Epstein, Verhan. Deutsch. Phys. Ges. 21 (1919) 96.
30. Z. Einstein, Ann. Phys. 69 (1922) H4, N20.
31. P.S. Epstein, Phys. Rev. 23 (1924) 710.
32. T.M. Brown, J. Phys. A 15 (1982) 2285.
33. Y. Alhassid, R.D. Levine, Phys. Rev. Lett. 57 (1986) 2879.
34. R. Dominguez-Cascante, D. Jou, J. Non-Equilib. Thermodyn. 20 (1995) 263.
35. F.H. Fröhner, Entropy maximization in nuclear physics, in: W.T. Grandy Jr., L.J. Schick (Ed.), Maximum Entropy and Bayesian Methods, Kluwer, Dordrecht, 1991.
36. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1984.
37. A. Fu, Astrophys. J. 323 (1987) 211.
38. W. Larecki, S. Piekarski, Nuovo Cimento D 13 (1991) 31; W. Larecki, Nuovo Cimento D 14 (1992) 141.
39. W. Larecki, S. Piekarski, Nuovo Cimento D 13 (1991) 31; W. Larecki, Nuovo Cimento D 14 (1992) 141.
40. J. Camacho, Phys. Rev. E 51 (1995) 220.
41. R. Dominguez, D. Jou, Phys. Rev. E 51 (1995) 158.
42. G.M. Kremer, I. Müller, J. Math. Phys. 33 (1992) 2265.
43. r and F given by Eqs. (17), (2) and (4), respectively.
44. G.C. Pomraning, The Equations of Radiation Hydrodynamics, Pergamon, Oxford, 1973.
45. S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, New York, 1967.
46. D. Mihalas, B.W. Mihalas, Foundations of Radiation Hydrodynamics, Oxford Univ. Press, Oxford, 1984.
47. J. Oxenius, Kinetic Theory of Particles and Photons, Springer, Berlin, 1986.
48. See, e.g., J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1975.
49. B. Robertson, Phys. Rev. 144 (1966) 151; 160 (1967) 175.
50. B. Robertson, Phys. Rev. 144 (1966) 151; 160 (1967) 175.
51. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics, Consultants Bureau, London, 1974.
52. R. Luzzi, A.R. Vasconcellos, Fortschr. Phys. 38 (1990) 887; A.R. Vasconcellos, R. Luzzi, L.S. García-Colín, Phys. Rev. A 43 (1991) 6622, 6633; J. Non-Equilib. Thermodyn. 20 (1995) 103, 119.
53. R. Luzzi, A.R. Vasconcellos, Fortschr. Phys. 38 (1990) 887; A.R. Vasconcellos, R. Luzzi, L.S. García-Colín, Phys. Rev. A 43 (1991) 6622, 6633; J. Non-Equilib. Thermodyn. 20 (1995) 103, 119.
54. R. Luzzi, A.R. Vasconcellos, Fortschr. Phys. 38 (1990) 887; A.R. Vasconcellos, R. Luzzi, L.S. García-Colín, Phys. Rev. A 43 (1991) 6622, 6633; J. Non-Equilib. Thermodyn. 20 (1995) 103, 119.
55. G.C. Pomraning, J. Quant. Spectrosc. Radiat. Transfer 27 (1982) 517.
56. J. Fort, J.E. Llebot, J. Phys. A 29 (1996) 3427.
57. v is Planckian, whereas (33) is not Planckian.
58. H.J. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations, Clarendon, Oxford, 1981.
59. M.R. Spiegel, Mathematical Handbook, McGraw-Hill, New York, 1968.
60. -1.
61. S. Geltman, Astrophys. J. 136 (1962) 935. See also, S. Chandrasekhar, Astrophys. J. 102 (1945) 223; S. Chandrasekhar, F.H. Breen, Astrophys. J. 104 (1946) 430; T.L. John, Astron. Astrophys. 193 (1988) 189.
62. S. Geltman, Astrophys. J. 136 (1962) 935. See also, S. Chandrasekhar, Astrophys. J. 102 (1945) 223; S. Chandrasekhar, F.H. Breen, Astrophys. J. 104 (1946) 430; T.L. John, Astron. Astrophys. 193 (1988) 189.
63. S. Geltman, Astrophys. J. 136 (1962) 935. See also, S. Chandrasekhar, Astrophys. J. 102 (1945) 223; S. Chandrasekhar, F.H. Breen, Astrophys. J. 104 (1946) 430; T.L. John, Astron. Astrophys. 193 (1988) 189.
64. S. Geltman, Astrophys. J. 136 (1962) 935. See also, S. Chandrasekhar, Astrophys. J. 102 (1945) 223; S. Chandrasekhar, F.H. Breen, Astrophys. J. 104 (1946) 430; T.L. John, Astron. Astrophys. 193 (1988) 189.
65. M.J. Berger, J. Hubbell, in: CRC Handbook of Chemistry and Physics, D.R. Lide (Ed.), CRC Press, Boca Raton, 1995, pp. 10-284.
66. -1 at the solar surface. These are the values we have used in order to estimate ε making use of Eq. (31).
67. B.C. Eu, K. Mao, Physica A 180 (1992) 65; 184 (1992) 187; K. Mao, B.C. Eu, Phys. Rev. A 48 (1993) 2471.
68. B.C. Eu, K. Mao, Physica A 180 (1992) 65; 184 (1992) 187; K. Mao, B.C. Eu, Phys. Rev. A 48 (1993) 2471.
69. B.C. Eu, K. Mao, Physica A 180 (1992) 65; 184 (1992) 187; K. Mao, B.C. Eu, Phys. Rev. A 48 (1993) 2471.
70. D. Jou, J. Casas-Vázquez, Phys. Rev. A 45 (1992) 8371.
71. W.G. Hoover, B.L. Holian, H.A. Posh, Phys. Rev. E 48 (1993) 3196.
72. K. Henjes, Phys. Rev. E 48 (1993) 3199.
73. D. Jou, J. Casas-Vázquez, Phys. Rev. E 48 (1993) 3201.
74. J. Casas-Vázquez, D. Jou, Phys. Rev. E 49 (1994) 1040.
75. B.C. Eu, L.S. García-Colín, Phys. Rev. E 54 (1996) 2501.
76. R. Luzzi, A.R. Vasconcellos, J. Casas-Vázquez, D. Jou, Physica A 234 (1997) 699.
77. See, e.g., J. Mathews, R.L. Walker, Mathematical Methods for Physics, Benjamin, Menlo Park, 1970.