In the domain of Statistical Mechanics of nonequilibrium-nonlinear (dissipative) systems based on a generalized Gibbs–Boltzmann ensemble formalism, it may be highlighted the so-called Nonequilibrium Statistical Operator Method, and, particularly, Zubarev’s approach. We report here a detailed analysis of a case consisting in a generalized nonequilibrium grand-canonical ensemble. Its construction requires to introduce besides the traditional densities of energy and the particle number their nonconserving-dissipative fluxes of all order. The description is quite appropriate to provide a framework for the construction of a nonclassical thermo-hydrodynamics, which is briefly described.
REFERENCES
1.
L. Tisza, in Thermodynamics: History and Philosophy, edited by K. Martinas, L. Ropolyi, and P. Szegedi (World Scientific, Singapore, 1991), pp. 515–522.
2.
3.
4.
L. S. Garcia-Colin, A. R. Vasconcellos, and R. Luzzi, J. Non-Equilib. Thermodyn. 19, 24 (1994); R. Luzzi, J. G. Ramos, and A. R. Vasconcellos, “Statistical-mechanical foundations of irreversible thermodynamics, IFGW-Unicamp Internal Report, 1997; and Fortschr. Phys./Prog. Phys. (submitted).
5.
M. A.
Tenan
, A. R.
Vasconcellos
, and R.
Luzzi
, Fortschr. Phys./Prog. Phys.
47
, 1
(1997
).6.
D. N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau–Plenum, New York, 1974).
7.
D. N. Zubarev, V. Morosov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes, Vol. 1: Basic Concepts, Kinetic Theory and Vol. 2: Relaxation and Hydrodynamic Processes (Akademie-Verlag, Berlin, 1996 and 1997, respectively).
8.
D. N.
Zubarev
and V. P.
Kalashnikov
, Math. Theor. Phys. (USSR)
1
, 108
(1970
).9.
R.
Luzzi
and A. R.
Vasconcellos
, Fortsch. Phys./Prog. Phys.
38
, 887
(1990
).10.
J. G.
Ramos
, A. R.
Vasconcellos
, and R.
Luzzi
, Fortsch. Phys./Prog. Phys.
43
, 265
(1995
).11.
E. T. Jaynes, in Frontiers of Nonequilibrium Physics, edited by G. T. Moore and M. O. Scully (Plenum, New York, 1986); also reprinted articles and notes in E. T. Jaynes Papers on Probability, Statistics and Statistical Physics, edited by D. Rosenkrantz (Reidel, Dordrecht, 1983).
12.
L.
Lauck
, A. R.
Vasconcellos
, and R.
Luzzi
, Physica A
168
, 789
(1990
).13.
J. R. Madureira, Phys. Rev. E (submitted).
14.
15.
D. Jou, J. Casas-Vázquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer, Berlin, 1993, 2nd ed. 1996).
16.
J. R.
Madureira
, A. R.
Vasconcellos
, R.
Luzzi
, J.
Casas-Vázquez
, and D.
Jou
, J. Chem. Phys.
108
, 7568
(1998
).17.
J. G. Ramos, A. R. Vasconcellos, and R. Luzzi, “A nonclassical generalized Navier–Stokes equation,” IFGW-Unicamp Internal Report, 1998, and future publications.
18.
V.
L’Vov
and I.
Procaccia
, Phys. World
1996
, 35
–40
.19.
20.
21.
22.
S. Sieniutycz, Conservation Laws in Variational Thermo-Hydrodynamics (Kluwer, Dordrecht, 1994); S. Sieniutycz and P. Salamon, Introductory article in Advances in Thermodynamics, Vol. 3: Nonequilibrium Theory and Extremum Principles, edited by the same authors (Taylor and Francis, New York, 1990).
23.
24.
25.
in Lecture Notes in Theoretical Physics, edited by W. E. Brittin, B. W. Downs, and J. Downs (Wiley-Interscience, New York, 1961), Vol. 3.
26.
27.
N. N. Bogoliubov, Lectures in Quantum Statistics (Gordon and Breach, New York, 1967, 1970), Vols. 1 and 2.
28.
N. N. Bogoliubov, in Studies in Statistical Mechanics I, edited by J. de Boer and G. E. Uhlenbeck (North-Holland, Amsterdam, 1962).
29.
G. E. Uhlenbeck, in Lectures in Statistical Mechanics, edited by M. Kac (Am. Math. Soc., Providence, RI, 1963).
30.
A. R.
Vasconcellos
, A. C.
Algarte
, and R.
Luzzi
, Physica A
166
, 517
(1990
).31.
W. T. Grandy, Foundation of Statistical Mechanics (Kluwer, Dordrecht, 1987, 1988), Vols. I and II.
32.
33.
34.
A. I. Akhiezer and S. V. Peletminskii, Methods of Statistical Physics (Pergamon, Oxford, 1981).
35.
H. Mori, I. Oppenheim, and J. Ross, in Studies in Statistical Mechanics, edited by J. de Boer and G. E. Uhlenbeck (North-Holland, Amsterdam, 1962).
36.
J. T.
Alvarez-Romero
and L. S.
Garcia-Colin
, Physica A
232
, 207
(1996
).37.
R. Luzzi, A. R. Vasconcellos, and J. G. Ramos, “A nonequilibrium statistical ensemble formalism: Basic concepts, construction, application, open questions and criticisms,” IFGW-Unicamp Internal Report, 1998; and Phys. Usp. (to be submitted).
38.
39.
H. Grabert, Projection Operator Techniques in Nonequilibrium Statistical Mechanics (Springer-Verlag, Berlin, 1982).
40.
J. G. Ramos, A. R. Vasconcellos, and R. Luzzi, “On the truncation process in IST,” IFGW-Unicamp Internal Report, 1997, and future publications.
41.
J. N. Kapur and H. K. Kesavan, Entropy Optimization Principles with Applications (Academic, San Diego, CA, 1992); see also articles in the Conference Proceedings, Maximum Entropy and Bayesian Methods, edited by W. T. Grandy and L. H. Schick (Kluwer, Dordrecht, 1991).
42.
43.
For example, B. Doubrovine, S. Novikov, and A. Fomenko, Géometrie Contemporaine (Mir, Moscow, 1985), Vol. I.
44.
S. V.
Peletminskii
and A. I.
Sokolovskii
, Theor. Math. Phys.
18
, 85
(1974
).45.
R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1953), Vol. I. pp. 184–186.
46.
A. R.
Vasconcellos
, R.
Luzzi
, and L. S.
Garcia-Colin
, Phys. Rev. A
43
, 6622
(1991
);A. R.
Vasconcellos
, R.
Luzzi
, and L. S.
Garcia-Colin
, Phys. Rev. A
43
, 6633
(1991
).47.
48.
S. P.
Heims
and E. T.
Jaynes
, Rev. Mod. Phys.
34
, 143
(1962
); (see subsection b, pp. 148–150 and Appendix B, p. 164 et seq.)49.
50.
See for example the review articles:
R.
Luzzi
and L. C.
Miranda
, Phys. Rep.
43
, 423
(1978
);R. Luzzi and A. R. Vasconcellos, in Semiconductors Probed by Ultrafast Laser Spectroscopy, Vol. 1, edited by R. Alfano (Academic, New York, 1984);
A. C.
Algarte
, A. R.
Vasconcellos
and R.
Luzzi
, Phys. Status Solidi B
173
, 487
(1992
).51.
52.
R.
Luzzi
, A. R.
Vasconcellos
, D.
Jou
, and J.
Casas-Vázquez
, J. Chem. Phys.
107
, 7383
(1997
).53.
R.
Luzzi
, A. R.
Vasconcellos
, J.
Casas-Vázquez
, and D.
Jou
, Physica A
248
, 111
(1997
).54.
R.
Balian
, Y.
Halhassid
, and H.
Reinhardt
, Phys. Rep.
131
, 1
(1986
).55.
J. R.
Madureira
, A. R.
Vasconcellos
, R.
Luzzi
, J.
Casas-Vázquez
, and D.
Jou
, J. Chem. Phys.
108
, 7580
(1998
).56.
A. C.
Algarte
, A. R.
Vasconcellos
, and R.
Luzzi
, Phys. Rev. B
54
, 11311
(1996
);and the third of Refs. 50.
57.
J. R.
Madureira
, A.R.
Vasconcellos
, R.
Luzzi
, and L.
Lauck
, Phys. Rev. E
57
, 3637
(1998
).58.
reprinted in The Collected Papers of J. C. Maxwell, edited by W. R. Niven (Dover, New York, 1965).
This content is only available via PDF.
© 1998 American Institute of Physics.
1998
American Institute of Physics
You do not currently have access to this content.
