The theory of irreversible processes: Foundations of a non-equilibrium statistical ensemble formalism

Rivista del Nuovo Cimento

Volumn 29, Issue 2, 2006, Pages 1-82

  Luzzi, R ^a   Vasconcellos, A R ^a   Ramos, J G ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846425757     PISSN: 0393697X     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncr/i2006-10009-1     Document Type: Review

References (259)

1. GIBBS J. W., Elementary Principles in Statistical Mechanics (Yale University Press, New Haven, USA) 1902; (Dover, New York, USA) 1960.
2. BOLTZMANN L., Vorlesungen über Gastheorie, Vols. 1 and 2 (Barth, Leipzig, Germany) 1896 and 1898. English translation by BRUSH S. G. (Univ. California Press, Berkeley, USA) 1964.
3. MAXWELL J. C., The Collected Papers of J. C. Maxwell, edited by NIVEN W. R. (Dover, New York, USA) 1965.
4. SKLAR L., Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics (Cambridge Univ. Press, Cambridge, UK) 1993.
5. JANCEL R., Foundations of Classical and Quantum Statistical Mechanics (Pergamon, Oxford, UK) 1969.
6. CASIMIR H. G. B., "On Onsager's principle of microscopic reversibility", Rev. Mod. Phys., 17 (1945) 343.
7. PENROSE O., "Foundations of statistical mechanics", Rep. Prog. Phys., 42 (1979) 1938.
8. KUBO R., "Oppening address at the Oji Seminar", Prog. Theor. Phys. (Jpn.), Suppl., 64 (1978) 1.
9. JAYNES E. T., Predictive Statistical Mechanics, in Frontiers of Non-equilibrium Statistical Physics, edited by MOORE G. T. and SCULLY M. O. (Plenum, New York, USA) 1986, pp. 33-55;
10. JAYNES E. T., Reprinted articles and additional notes in Jaynes Papers on Probability, Statistics, and Statistical Physics, edited by ROSENKRANTZ R. D. (Reidel-Kluwer, Dordrecht, The Netherlands) 1983.
11. DOUGHERTY J. P., Approaches to non-equilibrium statistical mechanics, in Maximum Entropy and Bayesian Method, edited by SKILLING J. (Kluwer Academic, Dordrecht, The Netherlands) 1989, pp. 131-6.
12. ZWANZIG R., Where do we go from here? in Perspectives in Statistical Physics, edited by RAVECHÈ H. J. (North Holland, Amsterdam, The Netherlands) 1981, p. 123.
13. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., Predictive Statistical Mechanics: A Non-equilibrium Ensemble Formalism (Kluwer Academic, Dordrecht, The Netherlands) 2002.
14. BOGOLIUBOV N. N., Problems of a dynamical theory in Statistical Physics, in Studies in Statistical Mechanics I, edited by DE BOER J. and UHLENBECK G. E. (North Holland, Amsterdam, The Netherlands) 1962.
15. PEIERLS R., Some simple remarks on the basis of transport theory, in Transport phenomena, Lecture Notes in Phys., Vol. 31, edited by EHLERS J., HEPP K. and WEIDENMÜLLER H. A. (Springer, Berlin, Germany) 1974.
16. KIRKWOOD J. G., "The statistical mechanical theory of transport processes", J. Chem. Phys., 14 (1946) 180.
17. MORI H., OPPENHEIM I. and ROSS J., Some topics in quantum statistics, in Studies in Statistical Mechanics I, edited by DE BOER J. and UHLENBECK G. E. (North Holland, Amsterdam, The Netherlands) 1962, pp. 217-98.
18. FANO U., "Description of states in quantum mechanics by density matrix and operator techniques", Rev. Mod. Phys., 29 (1957) 74.
19. BOGOLIUBOV N. N., Lectures in Quantum Statistics, Vols. 1 and 2 (Gordon and Breach, New York, USA) 1967 and 1970, respectively.
20. FEYNMAN R., Statistical Mechanics (Benjamin, Reading, USA) 1972.
21. KREUZER H. J., Non-equilibrium Thermodynamics and its Statistical Foundations (Clarendon, Oxford, UK) 1981.
22. BALESCU R., Equilibrium and Non-equilibrium Statistical Mechanics (Wiley-Interscience, New York, USA) 1975.
23. UHLENBECK G. E., The Boltzmann equation, in Lectures in Statistical Mechanics, edited by KAC M. (Am. Math. Soc., Providence, USA) 1963, pp. 183-203.
24. BALDIN A. M., KADYSHEVSKII V. G. and SISSAKIAN A. N., "Obituary: N. N. Bogoliubov", Phys. Today, 46 (1993) 101.
25. LOGUNOV A. A. and VLADIMOROV V. S., "N. N. Bogoliubov on his 70th birthday", Theor. Math. Phys., 40 (1980) 655.
26. SALAM A., VLADIMOROV V. S. and LOGUNOV A. A., "Tribute 'In memoriam of Nicolai N. Bogoliubov'", Theor. Math. Phys., 92 (1993) 817.
27. VLADIMOROV V. S. and LOGUNOV A. A., "N. N. Bogoliubov, Fifty years of scientific work", Theor. Math. Phys., 21 (1975) 1155.
28. ROBERTSON B., "Introduction to field operators in quantum mechanics", Am. J. Phys., 41 (1973) 678.
29. TAYLOR P. L., A Quantum Approach to the Solid State (Prentice-Hall, Englewood Cliffs, USA) 1970.
30. ZIMAN J. M., Elements of Advanced Quantum Theory (Cambridge Univ. Press, Cambridge, UK) 1969.
31. KRYLOV N. S., Works on the Foundations of Statistical Mechanics, with an Introduction by MIGDAL A. B. and FOCK V. A. (Princeton Univ. Press, Princeton, USA) 1979.
32. PRIGOGINE I., From Being to Becoming (Freeman, San Francisco, USA) 1980.
33. BOGOLIUBOV jr. N. N., A Method for Studying Model Hamiltonians (Pergamon, Oxford, UK) 1972.
34. ZUBAREV D. N., Non-equilibrium Statistical Thermodynamics (Consultants Bureau, New York, USA) 1974 [Neravnovesnaia Statisticheskaia Termodinamika (Izd. Nauka, Moscow, 1971)].
35. GELL-MANN M. and GOLDBERGER M. L., "The formal Theory of Scattering", Phys. Rev., 91 (1953) 398.
36. PRIGOGINE I., "Dissipative structures, dynamics, and entropy", Int. J. Quantum Chem., 9 (1975) 443.
37. LEBOWITZ J. L., "Boltzmann's Entropy and Time's Arrow", Phys. Today, 46 (1993) 32.
38. LEBOWITZ J. L., "Is Boltzmann's entropy time-arrow's archer?", Phys. Today (Letters), 47 (1994) 115.
39. ALVAREZ-ROMERO J. T. and GARCIA-COLIN L. S., "The foundations of informational statistical thermodynamics revisited", Physica A, 232 (1996) 207.
40. CHESTER G. V., "The theory of irreversible processes", Rep. Prog. Phys., 26 (1963) 411.
41. ZWANZIG R., Statistical mechanics of irreversibility, in Lectures in Theoretical Physics, edited by BRITTIN W. E., DOWNS B. W. and DOWNS J., Vol. 3 (Wiley-Interscience, New York, USA) 1961.
42. WEISS U., Quantum Dissipative Systems (World Scientific, Singapore) 1993.
43. MORI H., "Transport, collective motion, and Brownian motion", Progr. Theor. Phys. (Jpn.), 33 (1965) 423.
44. FEYNMAN R. P. and VERNON F. L., "The theory of a general quantum system interacting with a linear dissipative system", Ann. Phys. (N.Y.), 24 (1963) 118.
45. VAN HOVE L., "Correlations in space and time and Born approximation scattering in systems of interacting particles", Phys. Rev., 95 (1954) 249.
46. HASSAN S. A., VASCONCELLOS A. R. and LUZZI R., "The informational-statistical-entropy operator in a non-equilibrium ensemble formalism", Physica A, 262 (1999) 359.
47. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., Statistical Foundations of Irreversible Thermodynamics (Teubner-Bertelsmann Springer, Stuttgart, Germany) 2000.
48. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., "Irreversible Thermodynamics in a non-equilibrium statistical ensemble formalism", Riv. Nuovo Cimento, 24 (2001) 1.
49. TRUESDELL C., Rational Thermodynamics (McGraw-Hill, New York, USA) 1985; second enlarged edition (Springer, Berlin, Germany) 1988.
50. COURANT R. and HILBERT D., Methods of Mathematical Physics (Wiley-Interscience, New York, USA) 1953.
51. SKLAR L., Theory and Truth: Philosophical Critique within Foundational Science (Oxford Univ. Press, Oxford, UK); see also ref. [76].
52. RAMOS J. G., VASCONCELLOS A. R. and LUZZI R., "A non-equilibrium ensemble formalism: Criterion for truncation of description", J. Chem. Phys., 112 (2000) 2692.
53. VASCONCELLOS A. R., LUZZI R. and GARCIA- COLIN L. S., "A microscopic approach to Irreversible Thermodynamics I: General Theory", Phys. Rev. A, 43 (1991) 6622.
54. VASCONCELLOS A. R., LUZZI R. and GARCIA- COLIN L. S., "A microscopic approach to Irreversible Thermodynamics II: An example from semiconductor physics", Phys. Rev. A, 43 (1991) 6633.
55. ZWANZIG R., "Non-linear Transport Equations from Statistical Mechanics", Prog. Theor. Phys., Suppl. 64 (1978) 74.
56. GRABERT H., Projection Operator Techniques in Non-equilibrium Statistics (Springer, Berlin, Germany) 1981.
57. MCLENNAN J. A., "Statistical Theory of Transport Processes", in Adv. Chem. Phys., Vol. 5 (Academic, New York, USA) 1963, pp. 261-317.
58. PELETMINSKII S. V. and YATSENKO A. A., "Contribution to the quantum theory of kinetic and relaxation processes", JETP, 26 (1968) 773.
59. ROBERTSON B., "Equations of motion in non-equilibrium statistical mechanics", Phys. Rev., 144 (1966) 151.
60. ROBERTSON B., Application of maximum entropy to non-equilibrium statistical mechanics, in The Maximum Entropy Formalism (MIT Press, Cambridge, USA) 1978, pp. 289-320.
61. LAUCK L., VASCONCELLOS A. R. and LUZZI R., "A non-linear quantum transport theory", Physica A, 168 (1990) 789.
62. GRAD H., Principles of the kinetic theory of gases, in Handbuch der Physik XII, edited by FLÜGGE S. (Springer, Berlin, Germany) 1958, pp. 205-94.
63. LUZZI R. and VASCONCELLOS A. R., "The basic principles of irreversible thermodynamics in the context of an informational-statistical approach", Physica A, 241 (1997) 677.
64. CICCOTI G. and HOOVER W. G. (Editors), Molecular Dynamics Simulations of Statistical Mechanical Systems, Proc. Int. School of Physics "Enrico Fermi" (North Holland, Amsterdam, The Netherlands) 1986.
65. MARTIN P. C., Measurements and correlation functions, in Many-Body Physics, edited by WITT C. D. and BALIAN R. (Gordon and Breach, New York, USA) 1968, pp. 37-136.
66. ZUBAREV D. N., "Double-time Green functions in statistical physics", Uspekhi, 3 (1960) 320.
67. VASCONCELLOS A. R., MESQUITA M. V., RAMOS J. G. and LUZZI R., Response Function Theory and Generalized Fluctuation- Dissipation Theorem in a Non-equilibrium Ensemble Formalism, IFGW- Unicamp Internal Report, and future publication (2005).
68. VASCONCELLOS A. R., MESQUITA M. V., RAMOS J. G. and LUZZI R., Scattering Theory in a Non-equilibrium Ensemble Formalism, IFGW-Unicamp Internal Report, and future publication (2005).
69. GOULD S. J., Dinosaur in a Haystack (Random House, New York, USA) 1995.
70. ALFANO R. R. (Editor), Biological Events Probed by Ultrafast Laser Spectroscopy (Academic, New York, USA) 1982.
71. ALFANO R. R. (Editor), Semiconductors Probed by Ultrafast Laser Spectroscopy, Vols. 1 and 2 (Academic, New York, USA) 1984 and 1985, respectively.
72. ALFANO R. R., Frontiers of femtosecond and picosecond optical measuring techniques, in New Techniques and Ideas in Quantum Measurement Theory, edited by GREENBERGER D. M., Vol. 480 of NYAS Annals (New York Academy of Science, New York, USA) 1986, pp. 118-26.
73. DRIELS J. S. and RUDOLPH W., Ultrafast Laser Pulse Phenomena (Academic, New York, USA) 1996.
74. HARRIS C. B., IPPEN E. P., MOUROU G. A. and ZENWAIL A. H., Ultrafast Phenomena (Springer, Berlin, Germany) 1989.
75. HOPKINGS J. M. and SIBBET W., "Ultrashort-pulse lasers: Big payoffs in a flash", Scientific American, 283 (2000) 54.
76. BORN M., Experiment and Theory in Physics (Dover, New York, USA) 1956.
77. CUSHING J. T., Philosophical Concepts in Physics (Cambridge Univ. Press, Cambridge, UK) 1998.
78. HEISENBERG W., The Physical Conception of Nature (Hutchinson, London, UK) 1958.
79. HEISENBERG W., The notion of a "closed theory" in modern science, in Across the Frontiers, edited by ANSHEN R. N. (Harper and Row, New York, USA) 1975, pp. 39-46.
80. HAWKING S., The Nature of Space and Time (Princeton Univ. Press, Princeton, USA) 1996.
81. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., "A non-equilibrium statistical ensemble formalism. MaxEnt-NESOM: Basic concepts, construction, application, open questions and criticism", Int. J. Mod. Phys. B, 14 (2000) 3189.
82. RODRIGUES C. G., VASCONCELLOS A. R. and LUZZI R., "A Kinetic Theory for Non-linear Quantum Transport", Transp. Theor. Stat. Phys., 29 (2000) 733.
83. MAXWELL J. C., "On the dynamical theory of gases", Philos. Trans. R. Soc. (London), 157 (1867) 49.
84. JOU D., CASAS-VAZQUEZ J. and LEBON G., "Extended irreversible thermodynamics", Rep. Prog. Phys., 51 (1988) 1105.
85. FISHER R. A., "On the Mathematical Foundations of Theoretical Statistics", Philos. Trans. R. Soc. London A, 222 (1922) 309.
86. HAKEN H., Synergetics (Springer, Berlin, Germany) 1978.
87. STIX G., "Little big Science: An Overview (and articles thereafter)", Scientific American, 285 (2001) 26.
88. MEIXNER J., Thermodynamics of irreversible processes has many faces, in Irreversible Processes of Continuum Mechanics, edited by PARKUS H. and SEDOV L. (Springer, Wien, Austria) 1968, pp. 237-49.
89. BRUSH S. G., The Kind of Motion We Call Heat (North Holland, Amsterdam, The Netherlands) 1976.
90. DOUGAL A. A. and GOLDSTEIN L., "Energy exchange between electron and ion gases through Coulomb collisions in plasma", Phys. Rev., 109 (1958) 615.
91. LANDAU L. D., "The transport equation in the case of Coulomb interactions", Zh. Eksp. Teor. Fiz., 7 (1937) 203.
92. ABRAGAM A., The Principles of Nuclear Magnetism (Oxford University Press, Oxford, UK) 1961.
93. CASIMIR H. B. G. and DU PRE F. K., "Thermodynamic interpretation of paramagnetic relaxation phenomena", Physica, 5 (1938) 507.
94. WANG-CHANG C. S. and UHLENBECK G. E., The Kinetic Theory of Gases (North Holland, Amsterdam, The Netherlands) 1964.
95. FRÖHLICH H., "On the theory of dielectric breakdown in solids", Proc. R. Soc. (London) A, 188 (1947) 521.
96. SHKLOVSKII V. A., "Heating of electrons as the cause of hysteresis of the critical current in the resistive state of superconductors", Solid State, 17 (1976) 2040.
97. SHAH J. and LEITE R. C. C., "Radiative recombination from photoexcited hot carriers in GaAs", Phys. Rev. Lett., 22 (1969) 1304.
98. SHAH J., LEITE R. C. C. and SCOTT J. F., "Photoexcited hot LO phonons in GaAs", Solid State Commun., 8 (1970) 1089.
99. CASAS-VAZQUEZ J. and Jou D., "Non-equilibrium temperature versus local-equilibrium temperature", Phys. Rev. E, 49 (1994) 1040.
100. CASAS-VAZQUEZ J. and JOU D., "On a phenomenological non-equilibrium entropy for a class of rigid heat conductors", J. Phys. A: Math. Gen., 14 (1981) 1225.
101. JOU D., CASAS-VAZQUEZ J. and CRIADO-SANCHO M., Thermodynamics of Fluids under Flow (Springer, Berlin, Germany) 2001.
102. JOU D., CASAS-VAZQUEZ J. and LEBON G., "Questions and answers about a thermodynamic theory of the third type", Contemporary Phys., 33 (1992) 41.
103. JOU D., CASAS-VAZQUEZ J. and LEBON G., "Extended irreversible thermodynamics revisited", Rep. Prog. Phys., 62 (1999) 1035.
104. JOU D. and CASAS-VAZQUEZ J., "Possible experiment to check the reality of a non-equilibrium temperature", Phys. Rev. A, 45 (1992) 8371.
105. KEIZER J., "Fluctuations, stability, and generalized state functions at non-equilibrium steady states", J. Chem. Phys., 65 (1976) 4431.
106. KEIZER J., "Thermodynamics at non-equilibrium steady states", J. Chem. Phys., 69 (1978) 2609.
107. KEIZER J., "Heat, work, and the thermodynamic temperature at non-equilibrium steady states", J. Chem. Phys., 82 (1985) 2751.
108. KEIZER J., Statistical Thermodynamics of Irreversible Processes (Springer, Berlin, Germany) 1987.
109. MEIXNER J., Entropy and entropy production, in Foundations of Continuum Thermodynamics, edited by DELGADO J. J., NINA M. N. R. and WHITELAW J. H. (McMillan, London, UK) 1974, pp. 129-41.
110. MUSCHIK W., "Empirical foundation and axiomatic treatment of non-equilibrium temperature", Arch. Ration. Mech. Anal., 66 (1977) 379.
111. NETTLETON R. E., "On the relation between thermodynamic temperature and kinetic energy per particle", Can. J. Phys., 72 (1993) 106.
112. CASAS-VAZQUEZ J. and JOU D., "Temperature in Non-equilibrium Steady-Sates: A critical review of open problems and proposals", Rep. Prog. Phys., 66 (2003) 1937.
113. DE DONDER T., L'Affinite (Gauthier-Villars, Paris, France) 1936.
114. ONSAGER L., "Reciprocal relations in irreversible processes", Phys. Rev., 37 (1931) 405.
115. ONSAGER L. and MACHLUP S., "Fluctuations and irreversible processes I", Phys. Rev., 91 (1953) 1505.
116. ZUBAREV D. N., MOROSOV V. and RÖPKE R., Statistical Mechanics of Non-equilibrium Processes, Vol. 2; Relaxation and Hydrodynamic Processes (Akademie-Wiley VCH, Berlin, Germany) 1997.
117. GROOT S. DE and MAZUR P., Non-equilibrium Thermodynamics (North Holland, Amsterdam, The Netherlands) 1962.
118. PRIGOGINE I., Etude Thermodinamique des Phenomenes Irreversibles (Desoer, Liége, Belgium) 1947.
119. GLANSDORFF P. and PRIGOGINE I., Thermodynamic Theory of Structure, Stability, and Fluctuations (Wiley-Interscience, New York, USA) 1971.
120. ANDERSON P. W., "More is different: broken symmetry and nature of hierarchical structure of science", Science, 177 (1972) 393.
121. ANDERSON P. W., "Is Complexity Physics? Is it Science? What is it?" Phys. Today, 44 (1991) 9.
122. GELL-MANN M., "What is Complexity?" Complexity, 1 (1995) 16.
123. NICOLIS G. and PRIGOGINE I., Self-organization in Non-equilibrium Systems (Wiley-Interscience, New York, USA) 1977.
124. PRIGOGINE I., Structure, dissipation, and life, in From Theoretical Physics to Biology, edited by MAROIS M. (North Holland, Amsterdam, The Netherlands) 1969.
125. TISZA L., Concluding remarks, in Thermodynamics: History and Philosophy, edited by MARTINAS K., ROPOLYI L. and SZEGEDI P. (World Scientific, Singapore) 1991, pp. 515-22.
126. DRAGO A., The alternative content of thermodynamics, in Thermodynamics: History and Philosophy, edited by MARTINAS K., ROPOLYI L. and SZEGEDI P. (World Scientific, Singapore) 1991, pp. 329-45.
127. MARTINAS K., Aristotelian thermodynamics, in Thermodynamics: History and Philosophy, edited by MARTINAS K., ROPOLYI L. and SZEGEDI P. (World Scientific, Singapore) 1991, pp. 285-303.
128. EU B. C. and GARCIA-COLIN L. S., "Irreversible processes and temperature", Phys. Rev. E, 54 (1996) 2501.
129. EU B. C., "Form of uncompensated heat giving rise to a Pffafian differential form in thermodynamic space", Phys. Rev. E, 51 (1995) 768.
130. EU B. E., Non-equilibrium Statistical Mechanics: Ensemble Method (Kluwer Academic, Dordrecht, The Netherlands) 1998.
131. GARCIA-COLIN L. S. and RODRIGUEZ R. F., "On the relationship between extended irreversible thermodynamics and the wave approach to thermodynamics", J. Non-Equil. Thermodyn., 13 (1988) 81.
132. GARCIA-COLIN L. S. and URIBE F., "Extended irreversible thermodynamics beyond the linear regime: A critical overview", J. Non-Equil. Thermodyn., 16 (1991) 89-128.
133. GARCIA-COLIN L. S., "Extended non-equilibrium Thermodynamics, scope and limitations", Rev. Mex. Fis. (Mexico), 34 (1988) 344.
134. JOU D., CASAS-VAZQUEZ J. and LEBON G., Extended Irreversible Thermodynamics (Springer, Berlin, Germany) 1993. Second edition (Springer, Berlin, Germany) 1996; third enlarged edition (Springer, Berlin, Germany) 2001.
135. MÜLLER I. and RUGGERI T., Extended Thermodynamics (Springer, Berlin, Germany) 1993.
136. GRMELA M., "Thermodynamics of driven systems", Phys. Rev. E, 48 (1993) 919.
137. LANDSBERG P. T., "Foundations of thermodynamics", Rev. Mod. Phys., 28 (1956) 363.
138. LANDSBERG P. T., Thermodynamics with Quantum Statistical Illustration (Interscience, New York, USA) 1961.
139. HOBSON A., "Irreversibility and Information in Mechanical Systems", J. Chem. Phys., 45 (1966a) 1352.
140. HOBSON A., "Irreversibility in simple systems", Am. J. Phys., 34 (1966b) 411.
141. GRANDY W. T., Principles of Statistical Mechanics, Vols. 1 and 2 (Reidler-Kluwer, Dordrecht, The Netherlands) 1987 and 1988.
142. JAYNES E. T., "Information Theory and Statistical Mechanics I", Phys. Rev., 106 (1957) 620.
143. JAYNES E. T., "Information Theory and Statistical Mechanics II", Phys. Rev., 108 (1957) 171.
144. GARCIA-COLIN L. S., VASCONCELLOS A. R. and LUZZI R., "On informational statistical thermodynamics", J. Non-Equilib. Thermodyn., 19 (1994) 24.
145. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., "On the statistical foundations of irreversible thermodynamics", Fortschr. Phys./ Prog. Phys., 47 (1999) 401.
146. SIENIUTYCZ S. and SALAMON P., Introductory remarks in diversity of non-equilibrium theories and extremum principles, in Advances in Thermodynamics, edited by SIENIUTYCZ S. and SALAMON P., Vol. 3 (Taylor and Francis, New York, USA) 1990.
147. NETTLETON R. E., "Non-linear reciprocity in extended thermodynamics from the Robertson formalism", Euro. Phys. J. B, 17 (2000) 429.
148. NETTLETON R. E., "Statistical bases for extended thermodynamics of diffusion in dense fluids", J. Chem. Phys., 99 (1993) 3059.
149. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (I): General theory", Phys. Rev. A, 43 (1991) 6622.
150. NETTLETON R. E. and SOBOLEV S. L., "Applications of extended thermodynamics to chemical, rheological, and transport processes: A special survey", J. Non-Equil. Thermodyn., 19 (1995) 205.
151. TENAN M. A., VASCONCELLOS A. R. and LUZZI R., "Statistical foundations of generalized non-equilibrium thermodynamics", Fortschr. Phys./Prog. Phys., 47 (1997) 1.
152. NETTLETON R. E., "Reciprocity and consistency in non-local extended thermodynamics", Open Systems and Information Dynamics, 2 (1993) 41.
153. FREIDKIN E. S. and NETTLETON R. E., "Consistency between maximum-entropy formalism and H-theorem", Nuovo Cimenta B, 104 (1989) 597.
154. NETTLETON R. E., "Corrections to maximum entropy for steady-state conduction", J. Phys. A, 22 (1989) 5281.
155. NETTLETON R. E., "The Gibbs equation from maximum entropy", J. Chem. Phys., 93 (1990) 8247.
156. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (III): Generalized constitutive equations", J. Non-Equilib. Thermodyn., 20 (1995) 103.
157. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (IV): Diffusive and wave thermal motion", J. Non-Equilib. Thermodyn., 20 (1995) 119.
158. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (V): Memory-dependent constitutive equations", J. Mod. Phys., 9 (1995) 1933.
159. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (VI): Equations of evolution nonlinear in the fluxes in Informational Statistical Thermodynamics", J. Mod. Phys., 9 (1995) 1945.
160. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (VII): Response function theory for thermal perturbations in Informational Statistical Thermodynamics", Physica A, 221 (1995) 478.
161. VASCONCELLOS A. R., LUZZI R. and GARCIA-COLIN L. S., "A microscopic approach to Irreversible Thermodynamics (VIII): Diffusion and mobility and generalized Einstein relation", Physica A, 221 (1995) 495.
162. HAWKING S., The arrow of time, in 1990 - Yearbook of Science and the Future, (Encyclopaedia Britannica, Chicago, USA) 1989, pp. 44-53.
163. PRICE H., Time's Arrow and Archimedes' Point (Oxford Univ. Press, Oxford, UK) 1996.
164. ROSENFELD L., "On the foundations of statistical thermodynamics", Acta Phys. Polonica, 14 (1955) 3-29.
165. ROSENFELD L., Questions of irreversibility and ergodicity, in Proceedings of the International School of Physics "Enrico Fermi", Course XIV, edited by CALDIROLA P. (Academic, New York, USA) 1960, pp. 1-20.
166. ROSENFELD L., A question of physics, in Conversations in Physics and Biology, edited by BUCKLEY P. and PEAT D. (Univ. Toronto Press, Toronto, Canada) 1979.
167. DOUGHERTY J. P., "Explaining statistical mechanics", Stud. Philos. Sci., 24 (1993) 843.
168. DOUGHERTY J. P., "Foundations of non-equilibrium statistical mechanics", Philos. Trans. R. Soc. London A, 346 (1994) 259.
169. HASEGAWA H. H. and DRIEBE D. J., "Intrinsic irreversibility and the validity of the kinetic description of chaotic systems", Phys. Rev. E, 50 (1994) 1781.
170. MAKEY M. C., "The dynamic origin of increasing entropy", Rev. Mod. Phys., 61 (1989) 981.
171. NICOLIS G. and PRIGOGINE I., Exploring Complexity (Freeman, New York, USA) 1989.
172. BABLOYANTZ A., Molecules, Dynamics and Life: An Introduction to Self-Organization of Matter (Wiley, New York, USA) 1986.
173. NICOLIS G., Physics of far-from-equilibrium systems and self-organization, in The New Physics, edited by DAVIES P. (Cambridge Univ. Press, Cambridge, UK) 1989, pp. 316-47.
174. PRIGOGINE I. and STENGERS I., Order out of Chaos: Man's New Dialogue with Nature (Bantam, New York, USA) 1984.
175. FONSECA A. F., MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Informational-statistical thermodynamics of a complex system", J. Chem. Phys., 112 (2000) 3967.
176. MESQUITA M. V., VASCONCELLOS A. R., LUZZI R. and MASCARENHAS S., "Systems Biology", Braz. J. Phys., 34 (2004) 459.
177. MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Selective amplification of coherent polar vibrations in biopolymers", Phys. Rev. E, 48 (1993) 4049.
178. VASCONCELLOS A. R., MESQUITA M. V. and LUZZI R., "Complex behavior in biosystems: an information-theoretic approach", Chaos, Solitons, Fract., 11 (2000) 1313.
179. PENROSE R., Shadows of the Mind: A search for the missing science of consciousness (Oxford University Press, Oxford, UK) 1994.
180. MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Considerations on Fröhlich's non-equilibrium Bose-Einstein-like condensation", Phys. Lett. A, 238 (1998) 206.
181. MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Positive-feedback-enhanced Fröhlich's condensation in biosystems", Int. J. Quantum Chem., 66 (1998) 177.
182. MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Complexity in biological systems", Contemporary Physics, 40 (1999) 247.
183. LAUCK L., VASCONCELLOS A. R. and LUZZI R., "On Fröhlich's coherent effects in biological systems: Influence of carriers and high-order dissipative effects", J. Theor. Biol., 158 (1992) 1.
184. FRÖHLICH H., "Evidence for Bose-condensation-like excitation of coherent modes in biological systems", Phys. Lett. A, 51 (1975) 21.
185. SCOTT A. C., CHU F. Y. and MCLAUGHLIN S. W., "The soliton: A new concept in applied science", Proc. IEEE, 61 (1973) 1443.
186. HEGER A. J., KIVELSON S., SCHRIEFFER J. R. and SU W. P., "Solitons in conducting polymers" Rev. Mod. Phys., 60 (1988) 781.
187. HERSCHBACH D. R., The next 35 years of chemistry, The Sciences, Suppl, Fin-de-siècle perspectives (New York Academy of Sciences, New York, USA) 1996.
188. KIVELSON A. S., Soliton model of polyacetylene, in Solitons, edited by TRULLINGER S. E., ZAHKAROV V. E. and PROKOVSKY V. L. (Elsevier, New York, USA) 1986, pp. 301-87.
189. LEUTWYLER K., "Plastic power", Scientific American, 275 (1996) 25.
190. DAVYDOV A. S., "Theory of contraction of proteins under their excitation", J. Theor. Biol., 38 (1973) 559.
191. VASCONCELLOS A. R. and LUZZI R., "Vanishing thermal damping of Davydov's solitons", Phys. Rev. E, 48 (1993) 2246.
192. MESQUITA M. V., VASCONCELLOS A. R. and LUZZI R., "Near-dissipationless coherent excitations in biosystems", Int. J. Quantum Chem., 60 (1996) 689.
193. VASCONCELLOS A. R., MESQUITA M. V. and LUZZI R., "Solitary wave excitation in acetanilide", Phys. Rev. Lett., 80 (1998) 2008.
194. KLIMONTOVICH YU. L., "On the Need and the Possibility of a Unified Description of Kinetic and Hydrodynamic Processes", Theor. Math. Phys., 92 (1992) 909.
195. BURNETT D., "The Distribution of molecular velocities and the mean motion in a non-uniform gas", Proc. London Math Soc., 40 (1995) 382.
196. GUYER R. A. and KRUMHANSL J. A., "Solution of the linearized Boltzmann equation", Phys. Rev., 148 (1996) 766.
197. GARCIA-COLIN L. S., "On the Burnett and higher-order equations of hydrodynamics", Physica A, 118 (1983) 341.
198. HESS S., "On non-local constitutive relations, continued-fraction expansion for the wave vector dependent diffusion coefficient", Zeit. Naturforsh., 32 (1977) 678.
199. CHIU C-L. and THUNG N-C., "Maximum Velocity and Regularities in Open-Channel Flow", J. Hydraul. Eng., 126 (2002) 1.
200. WITTEN T. A., "Insights from soft condensed matter", Rev. Mod. Phys. (APS Centenary Issue) 71 (1999) S367.
201. KEE D. DE and WISSBRUN K. F., "Polymer Rheology", Phys. Today, 51 (1998) 24.
202. URIBE F. J., VELASCO R. M., GARCIA-COLIN L. S. and DIAZ-HERRERA, "Shock wave profiles in the Burnett approximation", Phys. Rev. E, 62 (2000) 6648.
203. URIBE F. J. and GARCIA-COLIN L. S., "Non-linear viscosity and Grad's methods", Phys. Rev. E, 60 (1999) 4052, and references therein.
204. MACKOWISKI D. W., PAPADOPOLUS D. H. and ROSNER D. E., "Comparison of Burnett and DSMC predictions of pressure distribution and normal stress in one-dimensional, strongly non-isothermal gases", Phys. Fluids, 11 (1999) 2108 and references therein.
205. BOBYLEV A. V., "The Chapman-Enskog and Grad methods for solving the Boltzmann equation", Doklady, 27 (1982) 29.
206. URIBE F. J., VELASCO R. M., GARCIA-COLIN L. S. and DIAZ-HERRERA, "Bobylev's instability", Phys. Rev. E, 62 (2000) 5835.
207. KARLIN I. V., "Exact summation of the Chapman-Enskog expansion from moment equation", J. Phys. A: Math. Gen., 33 (2000) 8037.
208. JOU D., CASAS-VAZQUEZ J., MADUREIRA J. R., VASCONCELLOS A. R. and LUZZI R., "Higher-order hydrodynamics: Extended Fick's law and evolution equation and Bobylev's instability", J. Chem. Phys., 116 (2001) 1571.
209. JOU D., CASAS-VAZQUEZ J., MADUREIRA J. R., VASCONCELLOS A. R. and LUZZI R., "Energy transport in a mesoscopic thermo-hydrodynamics", J. Mod. Phys., 15 (2001) 4211.
210. DEDEURWAERDERE T., CASAS-VÁZQUEZ J., JOU D. and LEBON G., "Foundations and applications of a mesoscopic thermodynamic theory of fast phenomena", Phys. Rev. E, 53 (1996) 498.
211. RAMOS J. G., VASCONCELLOS A. R., LUZZI R., Non-linear higher-order hydrodynamics: Generalized approach in a non-equilibrium ensemble formalism, IFGW-Unicamp Internal Report, and future publication (2005).
212. MONTROLL E. W. and SCHLESINGER M. F., "Maximum Entropy Formalism, Fractals, Scaling Phenomena and 1/f Noise: A Tale of Tails", J. Stat. Phys., 12 (1983) 209.
213. KAPUR J. N. and KESAVAN H. K., Entropy Optimization Principles with Applications (Academic, Boston, USA) 1992.
214. JEFFREYS H. Scientific Inference (Cambridge Univ. Press, Cambridge, UK) 1973, third edition.
215. KULLBACK S. and LEIBLER R. A., "On information and sufficiency", J Ann. Math. Stat., 22 (1951) 79.
216. CISZER I., "A class of measures of information of observation channels", Periodic Math. Hungarica, 9 (1972) 191 (see also ref. [214]).
217. JIZBA P. and ARIMITZU T., "The world according to Renyi", Ann. Phys. (N.Y.), 312 (2004) 17.
218. GRASSBERGER P. and PROCACCIA I., "Estimation of the Kolmogorov entropy from a chaotic signal", Phys. Rev. A, 28 (1983) 2591.
219. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., Competing Styles in Statistical Mechanics: I. Systematization and Clarification in a General Theory, E-print http://arXiv.org/abs/cond-mat/ 0306217 (2003) and future publication.
220. VASCONCELLOS A. R., RAMOS J. G. and LUZZI R., Competing Styles in Statistical Mechanics: II. Comparison of theory and experiment and further illustrations, E-print http://arXiv.org/abs/cond-mat/ 0306247 (2003).
221. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., On the question of auxiliary approaches in nonequilibrium statistical mechanics of complex systems, IFGW-Unicamp Internal Report and Ann. Phys. (NY), submitted (2006).
222. LANDSBERG P. T., "Entropies Galore!" Braz. J. Phys., 29 (1999) 46.
223. LANDSBERG P. T. and VEDRAL V., "Distributions and channel capacities in generalized statistical mechanics", Phys. Lett. A, 247 (1998) 322.
224. SHILLING J., in Maximum Entropy and Bayesian Methods in Science and Engineering, edited by ERIKSON G. J. and SMITH C. R. (Kluwer Academic, Dordrecht, The Netherlands) 1988.
225. KANIADAKIS G., "Non-linear kinetics underlying generalized statistics", Physica A, 296 (2001) 405.
226. KANIADAKIS G., "Statistical mechanics in the context of special relativity", Phys. Rev. E, 66 (2002) 56125 (17).
227. BECK C. and COHEN E. G. D., Superstatistics, E-print http://arXiv.org/abs/cond-mat/0205097 (2002).
228. BECK C. Superstatistics: Theory and Applications, E-print http://arXiv.org/abs/cond-mat/0303288 (2003).
229. VASCONCELLOS A. R., GORENSTEIN A., KLEINKE M. U., RAMOS J. G. and LUZZI R., "Statistical Approach to Fractal-Structured Physico-Chemical Systems: Analysis of Non-Fickian Diffusion", J. Mod. Phys. B, 20 (2006) 4821.
230. VASCONCELLOS A. R., LAURETO E., MENESES E. and LUZZI R., "Unconventional Statistical Mechanics Approach: Study of "anomalous" photoluminescence in semiconductor heterostructures", J. Mod. Phys. B, 18 (2004) 1743.
231. EBELING W., Entropy, predictability and historicity of nonlinear processes, in Statistical Physics And Thermodynamics of Nonlinear Non-equilibrium Systems, edited by EBELING W. and MUSCHIK W. (World Scientific, Singapore) 1993, pp. 217-28.
232. EBELING W., "On the relation between various entropy concepts and the caloric interpretation", Physica A, 182 (1992) 108.
233. FEISTEL R. and EBELING W., Evolution of Complex Systems (Kluwer Academic, Dordrecht, The Netherlands) 1989.
234. COX R. T., The Algebra of Probable Inference (Johns Hopkins Press, Baltimore, USA) 1961.
235. JAYNES E. T., Probability Theory: The Logic of Science (Cambridge Univ. Press, Cambridge, UK) 2003.
236. CHO A., "A fresh take on disorder or disorderly science?" Science, 297 (2002) 1268.
237. LUZZI R., VASCONCELLOS A. R. and RAMOS J. G., "Trying to make sense of disorder", Science, 298 (2002) 1171.
238. GRASSBERGER P., "Temporal scaling at Feigenbaum points and non-extensive thermodynamics", Phys. Rev. Lett., 95 (2005) 140601.
239. HAVRDA J. and CHARVAT F., "Quantification methods of classification processes: Concept of structural α-entropy", Kybernetica, 3 (1967) 036114.
240. NAUENBERG M., "A critique of q-entropy for thermal statistics", Phys. Rev. E, 67 (2003) 036114.
241. LAVENDA B. H., "On the definition of fluctuating temperature", Open Sys. & Information Dyn., 11 (2004) 139.
242. BALIAN R. and NAUENBERG M., "On 'non-extensive statistical mechanics: new trends, new perspectives' ", Europhys. News, 37 (2006) 9.
243. LUZZI R. VASCONCELLOS A. R. and RAMOS J. G., "On fallacies concerning nonextensive thermodynamics and q-entropy", Europhys. News, 37 (2006) 11.
244. BRILLOUIN L., Science and Information Theory (Academic, New York, USA) 1962.
245. JEFFREYS H., Probability Theory (Clarendon, Oxford, UK) 1961.
246. ANDERSON P. W., "The reverend Thomas Bayes, needles in a haystack, and the fifth force", Phys. Today, 45 (1992) 9.
247. JEFFREYS H., Scientific Inference (Cambridge Univ. Press, Cambridge, UK) 1973, third edition.
248. JAYNES E. T., Clearing up mysteries - The original goal, in Maximum Entropy and Bayesian Methods, edited by SHILLING J. (Kluwer Academic, Dordrecht, The Netherlands) 1989, pp. 1-13.
249. BRICMONT J., Science of Chaos or Chaos in Science? in The Flight from Science and Reason, edited by GROSS P. R., LEVITT N. and LEWIS M. W., Vol. 775 of NYAS Annals (New York Academy of Sciences, New York, USA) 1996, pp. 131-75.
250. PENROSE O., The direction of Time, in Chance in Physics: Foundations and Perspectives, edited by BRICMONT J. et al. (Springer, Berlin, Germany) 2001, pp. 61-82.
251. JAYNES E. T., "On the rationale of Maximum Entropy methods", Proc. IEEE, 70 (1982) 939.
252. BRUSHVILI L. L. and ZVIADADZE M. D., "On the quasi-thermodynamic theory of magnetic relaxation", Physica, 59 (1972) 679.
253. VASCONCELLOS A. R., ALGARTE A. C. and LUZZI R., "On the question of Bogoliubov's hierarchy of relaxation times: An example from semiconductor physics", Physica A, 166 (1990) 517.
254. ZUBAREV D. N., MOROZOV V. N. and RÖPKE G., Statistical Mechanics of Nonequilibrium Processes, Vols. I and II (Akademie Verlag-Wiley VCH, Berlin, Germany) 1996.
255. AKHIEZER A. I. and PELETMINSKII S. V., Methods of Statistical Physics (Pergamon, Oxford, UK) 1981.
256. GRANDY W. T., "Principle of maximum entropy and irreversible processes", Phys. Rep., 62 (1980) 175.
257. FORSTER D., Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, Readings, USA) 1975.
258. PELETMINSKII S. V. and SOKOLOVSKII A. I., "Flux operators of physical variables and the method of quasi-averages", Theor. Math. Phys., 18 (1974) 85.
259. ANDRADE NETO A. V., VASCONCELLOS A. R., LUZZI R. and FREIRE V. N., "A Raman scattering-based method to probe the carrier drift velocity in semiconductors: Application to GaN", Appl. Phys. Lett, 85 (2004) 4055.