Non-equilibrium Statistical Mechanics

  • David Jou
  • José Casas-Vázquez
  • Georgy Lebon


In the preceding chapter we discussed the microscopic foundations of extended irreversible thermodynamics through fluctuation theory. The present chapter deals with more general methods of non-equilibrium statistical mechanics. First, we start from the Liouville equation and introduce the projection operator technique to relate the memory function to the time correlation function of the fluctuations of the fluxes, a key result in modem non-equilibrium statistical mechanics. This result is of special interest in EIT, because it emphasizes the role played by the evolution of the fluctuations of the thermodynamic fluxes. Furthermore, the method of projection operators is useful, since it provides an explicit method for formulating the dynamical equations of the basic variables. Classically, the set of variables consists of the conserved slow variables (energy, linear momentum, mass) and some order parameters characterizing second-order phase transitions. Here we shall present a generalization of this method by adding the dissipative fast fluxes to the basic set of variables.


Heat Flux Lagrange Multiplier Irreversible Thermodynamic Pressure Tensor Viscous Pressure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 5.1.
    P. Résibois and M. de Leener, Classical Kinetic Theory of Fluids,Wiley, New York, 1977.Google Scholar
  2. 5.2.
    D. A. McQuarrie, Statistical Mechanics, Harper and Row, New York, 1976.Google Scholar
  3. 5.3..
    B. J. Berne in Statistical Mechanics (Part B: Time-Dependent Processes) (B. J. Berne, ed.), Plenum, New York, 1977.Google Scholar
  4. 5.4.
    H. Grabert, Projection Operator Techniques in Non-equilibrium Statistical Mechanics, Springer, Berlin, 1981.Google Scholar
  5. 5.5.
    A. Z. Akcasu and E. Daniels, Phys. Rev. A 2 (1970) 962ADSCrossRefGoogle Scholar
  6. M. Grant and R. Desai, Phys. Rev. A 25 (1982) 2727.ADSCrossRefGoogle Scholar
  7. 5.6.
    E. T. Jaynes in Statistical Physics (W. K. Ford, ed.), Benjamin, New York, 1963.MATHGoogle Scholar
  8. 5.7.
    R. D. Levine and M. Tribus (eds), The Maximum Entropy Formalism, MIT Press, Cambridge, Mass., 1979.MATHGoogle Scholar
  9. 5.8.
    D. N. Zubarev, Nonequilibrium Statistical Mechanics, Consultants Bureau, London, 1974.Google Scholar
  10. 5.9.
    W. T. Grandy, Jr., Phys. Rep. 62 (1980) 175MathSciNetADSCrossRefGoogle Scholar
  11. F. Schlögl, Phys. Rep. 62 (1980) 267ADSCrossRefGoogle Scholar
  12. J. Galvao Ramos, A. R. Vasconcellos, and R. Luzzi, Fortschr. Phys. 43 (1995) 265.MathSciNetMATHCrossRefGoogle Scholar
  13. 5.10.
    B. Robertson, Phys. Rev. 160 (1967) 175.ADSCrossRefGoogle Scholar
  14. 5.11.
    A. R. Vasconcellos, R. Luzzi, and L. S. García-Colín, Phys. Rev. A 43 (1991) 6622, 6633.ADSCrossRefGoogle Scholar
  15. 5.12.
    M. Ichiyanagi, J. Phys. Soc. Japan 59 (1990) 1970MathSciNetADSCrossRefGoogle Scholar
  16. M. Ichiyanagi, Prog. Theor. Phys. 84 (1991) 810.ADSCrossRefGoogle Scholar
  17. 5.13.
    Z. Banach, Physica A 159 (1987) 343ADSCrossRefGoogle Scholar
  18. R. E. Nettleton, Phys. Rev. A 42 (1990) 4622ADSCrossRefGoogle Scholar
  19. R. E. Nettleton, J. Chem. Phys 93 (1990) 81CrossRefGoogle Scholar
  20. B. C. Eu, Physica A 171 (1991) 285.ADSCrossRefGoogle Scholar
  21. 5.14.
    A. B. Corbet, Phys. Rev. A 9 (1974) 1371ADSCrossRefGoogle Scholar
  22. R. M. Nisbet and W. S. C. Gurney, Phys. Rev. A 10 (1974) 720.ADSCrossRefGoogle Scholar
  23. 5.15.
    D. Jou, C. Pérez-García, and J. Casas-Vazquez, J. Phys. A 17 (1984) 2799MathSciNetADSCrossRefGoogle Scholar
  24. R. E. Nettleton, J. Phys. A 21 (1988) 3939.ADSMATHCrossRefGoogle Scholar
  25. 5.16.
    A. M. S. Tremblay, E. D. Siggia, and M. R. Arai, Phys. Rev. A 23 (1981) 1451ADSCrossRefGoogle Scholar
  26. R. Schmitz, Phys. Rep. 171 (1988) 1ADSCrossRefGoogle Scholar
  27. A. M. S. Tremblay in Recent Developments in Nonequilibrium Thermodynamics (J. Casas-Vazquez, D. Jou, and G. Lebon, eds.), Springer, Berlin, 1984.Google Scholar
  28. 5.17.
    D. Jou, J. E. Llebot, and J. Casas-Vazquez, Phys. Rev. A 25 (1982) 508ADSCrossRefGoogle Scholar
  29. D. Jou and T. Careta, J. Phys. A 15 (1982) 3195ADSCrossRefGoogle Scholar
  30. R. E. Nettleton, J. Chem. Phys. 81 (1984) 2458.ADSCrossRefGoogle Scholar
  31. 5.18.
    E. Jahnig and P. H. Richter, J. Chem. Phys. 64 (1976) 4645ADSCrossRefGoogle Scholar
  32. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes,Springer, Berlin, 1987.CrossRefGoogle Scholar
  33. 5.19.
    H. Spohn and J. L. Lebowitz, Comm. Math. Phys. 54 (1977) 97.MathSciNetADSCrossRefGoogle Scholar
  34. 5.20.
    B. N. Miller and P. M. Larson, Phys. Rev A 20 (1979) 1717.ADSCrossRefGoogle Scholar
  35. 5.21.
    H. Goldstein, Classical Mechanics, 2nd edn, Addison-Wesley, Reading, Mass., 1975.MATHGoogle Scholar
  36. 5.22.
    J. Camacho, Phys. Rev. E 51 (1995) 220.ADSCrossRefGoogle Scholar
  37. 5.23.
    H. Fröhlich, Riv. Nuovo Cimento 7 (1977) 399MathSciNetCrossRefGoogle Scholar
  38. H. Fröhlich and F. Kremer, eds, Coherent excitations in biological systems, Springer, Berlin, 1983Google Scholar
  39. 5.24.
    M. Ferrer and D. Jou, Am. J. Phys. 63 (1995) 237ADSCrossRefGoogle Scholar
  40. 5.25.
    D. Mihalas and B. W. Mihalas, Foundations of Radiation Hydrodynamics, Oxford University Press, Oxford, 1985Google Scholar
  41. A. M. Anile, S. Permisi, and M. Sanmartino, J. Math. Phys. 32 (1991) 544.MathSciNetADSMATHCrossRefGoogle Scholar
  42. 5.26.
    W. Larecki, Nuovo Cimento D 14 (1993) 141.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • David Jou
    • 1
  • José Casas-Vázquez
    • 1
  • Georgy Lebon
    • 2
  1. 1.Departament de FísicaUniversitat Autònoma de Barcelona, Grup de Física EstadísticaBellaterra, CataloniaSpain
  2. 2.Département de PhysiqueUniversité de LiègeLiègeBelgium

Personalised recommendations