Entropy in nonequilibrium statistical mechanics

Journal of the Physical Society of Japan

Volumn 75, Issue 11, 2006, Pages

  Kita, Takafumi ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Boltzmann equation; Dyson equation; Entropy; H theorem; Keldysh Green's function; Nonequilibrium statistical mechanics; Wigner representation

Indexed keywords

EID: 33847301595     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJ.75.114005     Document Type: Article

References (46)

1. P. Glansdorff and I. Prigogine: Thermodynamic Theory of Structure, Stability and Fluctuations (John Wiley & Sons, New York, 1971).
2. H. Haken: Rev. Mod. Phys. 47 (1975) 67.
3. Y. Kuramoto: Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
4. M. C. Cross and P. C. Hohenberg: Rev. Mod. Phys. 65 (1993) 851.
5. R. Kubo: J. Phys. Soc. Jpn. 12 (1957) 570.
6. D. N. Zubarev: Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974).
7. J. W. Gibbs: Elementary Principles in Statistical Mechanics (Yale University Press, New Haven, 1902).
8. L. D. Landau and E. M. Lifshitz: Statistical Physics (Pergamon, Oxford, 1980).
9. C. Cercignani: Ludwig Boltzmann: The Man Who Trusted Atoms (Oxford University Press, Oxford, 1998).
10. S. Chapman and T. G. Cowling: The Mathematical Theory of Non-uniform Gases (Cambridge University Press, Cambridge, 1990).
11. J. O. Hirschfelder, C. F. Curtiss and R. B. Bird: Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
12. C. Cercignani: The Boltzmann Equation and Its Applications (Springer-Verlag, New York, 1988).
13. 10) but naturally results from the high-temperature expansion of the quantum statistical expression.
14. Yu. B. Ivanov, J. Knoll and D. N. Voskresensky: Nucl. Phys. A 657 (1999) 413.
15. Yu. B. Ivanov, J. Knoll and D. N. Voskresensky: Nucl. Phys. A 672 (2000) 313.
16. L. V. Keldysh: Zh. Eksp. Teor. Fiz. 47 (1964) 1515
17. [Sov. Phys. JETP 20 (1965) 1018].
18. L. P. Kadanoff and G. Baym: Quantum Statistical Mechanics (Benjamin, New York, 1962).
19. J. W. Serene and D. Rainer: Phys. Rep. 101, 221 (1983).
20. J. Rammer and H. Smith: Rev. Mod. Phys. 58 (1986) 323.
21. W. Botermans and R. Malfliet: Phys. Rep. 198 (1990) 115.
22. M. Levanda and V. Fleurov: J. Phys.: Condens. Matter 6 (1994) 7889.
23. H. Huag and A.-P. Jauho: Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1998).
24. T. Kita: Phys. Rev. B 64 (2001) 054503.
25. T. Kita: J. Phys. Soc. Jpn. 68 (1999) 3740.
26. S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, 1961).
27. F. H. Busse: Rep. Prog. Phys. 41 (1978) 1929.
28. V. Croquette: Comtemp. Phys. 30 (1989) 113;
29. V. Croquette: Comtemp. Phys. 30 (1989) 153.
30. E. L. Koschmieder: Bénard Cells and Taylor Vortices (Cambridge University Press, Cambridge, 1993).
31. J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell and G. Ahlers: Rev. Sci. Instrum. 67 (1996) 2043.
32. E. Bodenschatz, W. Pesch and G. Ahlers: Annu. Rev. Fluid Mech. 32 (2000) 709.
33. R. Graham: in Order and Fluctuations in Equilibrium and Non-equilibrium Statistical Mechanics, ed. G. Nicolis, G. Dewel and J. W. Turner (John Wiley & Sons, New York, 1981) p. 235.
34. D. Kondepudi and I. Prigogine: Modern Thermodynamics (John Wiley & Sons, New York, 1998) Chap. 18.2.
35. J. M. Luttinger and J. C. Ward: Phys. Rev. 118 (1960) 1417.
36. A. A. Abrikosov, L. P. Gor'kov and I. E. Dzyaloshinski: Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, New Jersey, 1963).
37. A. L. Fetter and J. D. Walecka: Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
38. G. Baym: Phys. Rev. 127 (1962) 1391.
39. G. M. Carneiro and C. J. Pethick: Phys. Rev. B 11 (1975) 1106.
40. J. M. Luttinger: Phys. Rev. 119 (1960) 1153.
41. G. Baym and L. Kadanoff: Phys. Rev. 124 (1961) 287.
42. A. I. Larkin and Y. N. Ovchinnikov: Zh. Eksp. Teor. Fiz. 68 (1975) 1915
43. [Sov. Phys. JETP 41 (1975) 960].
44. J. Orban and A. Bellemans: Phys. Lett. A 24 (1967) 620.
45. We should point out the difference between the present paper and ref. 24 that the total particle number (the chemical potential) is chosen as an independent variable in the present paper (ref. 24).
46. P. Fulde and H. Wagner: Phys. Rev. Lett. 27 (1971) 1280.