Skip to main content
SpringerLink
Log in

Statistical Irreversible Thermodynamics in the Framework of Zubarev’s Nonequilibrium Statistical Operator Method

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We describe the formalism of statistical irreversible thermodynamics constructed based on Zubarev’s nonequilibrium statistical operator (NSO) method, which is a powerful and universal tool for investigating the most varied physical phenomena. We present brief overviews of the statistical ensemble formalism and statistical irreversible thermodynamics. The first can be constructed either based on a heuristic approach or in the framework of information theory in the Jeffreys-Jaynes scheme of scientific inference; Zubarev and his school used both approaches in formulating the NSO method. We describe the main characteristics of statistical irreversible thermodynamics and discuss some particular considerations of several authors. We briefly describe how Rosenfeld, Bohr, and Prigogine proposed to derive a thermodynamic uncertainty principle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. W. Anderson, “More is different: Broken symmetry and the nature of the hierarchical structure of science,” Science, 4047, 393–396 (1972).

    Article  ADS  Google Scholar 

  2. P. W. Anderson, “Is complexity physics? Is it science? What is it?” Phys. Today, 44, No. 7, 9–10 (1991).

    Article  Google Scholar 

  3. R. Luzzi and A. R. Vasconcellos, “Complex behavior in condensed matter: Morphological order in dissipative carrier system,” Complexity, 2, 42–49 (1997).

    Article  Google Scholar 

  4. M. V. Mesquita, A. R. Vasconcellos, and R. Luzzi, “Complexity in biological systems,” Contemp. Phys., 40, 247–256 (1999).

    Article  ADS  Google Scholar 

  5. G. Nicolis and I. Prigogine, Exploring Complexity: An Introduction, Freeman, New York (1989).

    Google Scholar 

  6. R. Luzzi, A. R. Vasconcellos, and J. G. Ramos, Statistical Foundations of Irreversible Thermodynamics (Teubner Texts Phys., Vol. 35), Teubner, Stuttgart (2000).

    Google Scholar 

  7. P. T. Landsberg, “Foundations of thermodynamics,” Rev. Modern Phys., 28, 363–392 (1956).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. A. Hobson, “Irreversibility and information in mechanical systems,” J. Chem. Phys., 45, 1352–1357 (1966).

    Article  ADS  Google Scholar 

  9. B. C. Eu, Kinetic Theory of Irreversible Thermodynamics, Wiley, New York (1992).

    Google Scholar 

  10. R. V. Velasco and L. S. Garcia-Colin, “The kinetic foundations of non-local nonequilibrium thermodynamics,” J. Non-Equilib. Thermodyn., 18, 157 (1993).

    Article  ADS  MATH  Google Scholar 

  11. R. E. Nettleton, “Generalized Grad-type foundations for nonlinear extended thermodynamics,” Phys. Rev. A, 42, 4622–4629 (1990).

    Article  ADS  Google Scholar 

  12. L. S. García-Colín, M. López de Haro, R. F. Rodríguez, J. Casas-Vázquez, and D. Jou, “On the foundations of extended irreversible thermodynamics,” J. Statist. Phys., 37, 465–484 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  13. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York (1974).

    Google Scholar 

  14. D. N. Zubarev, “The method of the non-equilibrium statistical operator and its application: I. The nonequilibrium statistical operator,” Fortschr. Physik, 18, 125–147 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  15. D. N. Zubarev, J. Soviet Math., 16, 1509–1571 (1981).

    Article  Google Scholar 

  16. D. N. Zubarev, “Modern methods of the statistical theory of nonequilibrium processes,” J. Soviet Math., 16, 1509–1571 (1981).

    Article  MATH  Google Scholar 

  17. R. Luzzi, Á. R. Vasconcellos, and J. Galväo Ramos, Predictive Statistical Mechanics: A Nonequilibrium Statistical Ensemble Formalism (Fund. Theor. Phys., Vol. 122), Kluwer, Dordrecht (2002).

    Google Scholar 

  18. D. N. Zubarev, V. G. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes, Vol. 1, Basic Concepts, Kinetic Theory, Akademie, Berlin (1996).

    MATH  Google Scholar 

  19. D. N. Zubarev, V. G. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes, Vol. 2, Relaxation and Hydrodynamic Processes, Akademie, Berlin (1997).

    MATH  Google Scholar 

  20. A. I. Akhiezer and S. V. Peletminskii, Methods of Statistical Physics [in Russian], Nauka, Moscow (1977); English transl., Pergamon, Oxford (1981).

    Google Scholar 

  21. J. A. McLennan, “The formal statistical theory of transport processes,” in:Advances in Chemical Physics (I. Prigogine, ed.), Vol. 5, Acad. Press, New York (1963), pp. 261–317.

    Google Scholar 

  22. W. T. Grandy, Principles of Statistical Mechanics, Vol. 1, Equilibrium Theory, Reidel, Dordrecht (1987).

    MATH  Google Scholar 

  23. W. T. Grandy, Principles of Statistical Mechanics, Vol. 2, Nonequilibrium Phenomena, Reidel, Dordrecht (1988).

    MATH  Google Scholar 

  24. B. Robertson, “Equations of motion in nonequilibrium statistical mechanics,” Phys. Rev., 144, 151–161 (1996).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. J. P. Dougherty, “Foundations of non-equilibrium statistical mechanics,” Philos. Trans. Roy. Soc. London Ser. A, 346, 259–305 (1994).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. R. Luzzi and A. R. Vasconcellos, “On the nonequilibrium statistical operator method,” Fortschr. Phys., 38, 887–922 (1990).

    Article  MathSciNet  Google Scholar 

  27. R. Zwanzig, “Where do we go from here?” in: Perspectives in Statistical Mechanics (H. J. Raveché, ed.), North Holland, Amsterdam (1981), pp. 123–124.

    Google Scholar 

  28. J. G. Kirkwood, “The statistical mechanical theory of transport processes I: General theory,” J. Chem. Phys., 14, 180–201 (1946).

    Article  ADS  Google Scholar 

  29. M. S. Green, “Markoff random processes and the statistical mechanics of time-dependent phenomena,” J. Chem. Phys., 20, 1281–1295 (1952).

    Article  ADS  MathSciNet  Google Scholar 

  30. H. Mori, I. Oppenheim, and J. Ross, “Some topics in quantum statistics: The Wigner function and transport theory,” in: Studies in Statistical Mechanics (J. de Boer and G. E. Uhlenbeck, eds.), Vol. 1, North Holland, Amsterdam (1962), pp. 213–298.

    Google Scholar 

  31. H. Mori, “Transport, collective motion, and Brownian motion,” Prog. Theoret. Phys., 33, 423–455 (1965).

    Article  ADS  MATH  Google Scholar 

  32. R. Zwanzig, “Statistical mechanics of irreversibility,” in: Lectures in Theoretical Physics (W. E. Brittin, B. W. Downs, and J. Downs, eds.), Vol. 3, Wiley-Interscience, New York (1961), pp. 106–141.

    Google Scholar 

  33. N. N. Bogoliubov, Problems of a Dynamical Theory in Statistical Physics [in Russian], Gostekhizdat, Moscow (1946); English transl.: “Problems of a dynamical theory in statistical physics,” in: Studies in Statistical Physics (J. de Boer and G. E. Uhlenbeck, eds.), Vol. 1, North Holland, Amsterdam (1962), pp. 12–118.

    Google Scholar 

  34. R. Peierls, “Some simple remarks on the basis of transport theory,” in: Transport Phenomena (Lect. Notes Phys., Vol. 31, G. Kirczenow and J. Marro, eds.), Springer, Berlin (1974), pp. 1–33.

    Google Scholar 

  35. U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev.Modern Phys., 29, 74–93 (1957).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. B. Robertson, “Introduction to field operators in quantum mechanics,” Amer. J. Phys., 41, 678–690 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  37. R. P. Feynman, Statistical Mechanics, Benjamin, Reading, Mass. (1972).

    Google Scholar 

  38. P. L. Taylor, A Quantum Approach to the Solid State, Prentice Hall, Englewood Cliffs, N. J. (1970).

    Google Scholar 

  39. J. M. Ziman, Elements of Advanced Quantum Theory, Cambridge Univ. Press, Cambridge (1969).

    MATH  Google Scholar 

  40. J. Klauder and B. Skagerstam, Coherent States, World Scientific, Singapore (1984).

    Google Scholar 

  41. N. Hugenholtz, “Applications of field theoretical methods to many-boson systems [Lecture 3],” in: 1962 Cargèse Lectures in Theoretical Physics (M. Lévy, ed.), Benjamin, New York (1963).

    Google Scholar 

  42. N. S. Krylov, Works on Foundations in Statistical Physics [in Russian], Acad. Sci. USSR, Moscow (1950); English transl., Princeton Univ. Press, Princeton (1979).

    Google Scholar 

  43. N. N. Bogoliubov, Lectures in Quantum Mechanics, Vol. 1, Gordon and Breach, New York (1967).

    MATH  Google Scholar 

  44. N. N. Bogoliubov, Lectures in Quantum Mechanics, Vol. 2, Gordon and Breach, New York (1970).

    Google Scholar 

  45. A. Salam, V. S. Vladimorov, and A. A. Logunov, “In memory of Nikolai Nikolaevich Bogolyubov (08.21.1909–02.13.1992),” Theor. Math. Phys., 92, 817–819 (1992).

    Article  Google Scholar 

  46. L. Lauck, Á. R. Vasconcellos, and R. Luzzi, “A nonlinear quantum transport theory,” Phys. A, 168, 789–819 (1990).

    Article  Google Scholar 

  47. J. R. Madureira, Á. R. Vasconcellos, R. Luzzi, and L. Lauck, “Markovian kinetic equations in a nonequilibrium statistical ensemble formalism,” Phys. Rev. E, 57, 3637–3640 (1998).

    Article  ADS  Google Scholar 

  48. J. R. Madureira, A. R. Vasconcellos, R. Luzzi, J. Casas-Vazquez, and D. Jou, “Evolution of dissipative processes via a statistical thermodynamic approach: I. Generalized Mori–Heisenberg–Langevin equations,” J. Chem. Phys., 108, 7568–7579 (1998).

    Article  ADS  Google Scholar 

  49. J. G. Ramos, A. R. Vasconcellos, and R. Luzzi, “A classical approach in predictive statistical mechanics: A generalized Boltzmann formalism,” Fortschr. Phys., 43, 265–300 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  50. F. S. Vannucchi, Á. R. Vasconcellos, and R. Luzzi, “Thermo-statistical theory of kinetic and relaxation processes,” Internat. J. Modern Phys. B, 23, 5283–5305 (2009).

    Article  ADS  MATH  Google Scholar 

  51. B. Robertson, “Equations of motion in nonequilibrium statistical mechanics: II. Energy transport,” Phys. Rev., 160, 175–183 (1967); Erratum, 166, 206 (1968).

    Article  ADS  Google Scholar 

  52. C. A. B. Silva, Á. R. Vasconcellos, J. G. Ramos, and R. Luzzi, “Generalized kinetic equations for far-from-equilibrium many-body systems,” J. Statist. Phys., 143, 1020–1034 (2011).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. H. Spohn, “Kinetic equations from Hamiltonian dynamics: Markovian limits,” Rev. Modern Phys., 52, 569–615 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  54. Y. L. Klimontovich, Statistical Theory of Open Systems [in Russian], TOO “Yanus,” Moscow (1995); English transl.: Vol. 1, A Unified Approach to Kinetic Description of Processes in Active Systems (Fund. Theor. Phys., Vol. 67), Kluwer Academic, Dordrecht (1995).

    Book  MATH  Google Scholar 

  55. W. M. Elsasser, “On quantum measurements and the role of the uncertainty relations in statistical mechanics,” Phys. Rev., 52, 987–999 (1937).

    Article  ADS  MATH  Google Scholar 

  56. E. T. Jaynes, “A backward look to the future,” in: Physics and Probability (W. T. Grandy and P. W. Milonni, eds.), Cambridge Univ. Press, Cambridge (1993), pp. 261–275.

    Chapter  Google Scholar 

  57. E. T. Jaynes, “Notes on present status and future prospects,” in: Maximum Entropy and Bayesian Methods (Fund. Theor. Phys., Vol. 43, W. T. Grandy and L. H. Schick, eds.), Springer, Netherlands (1991), pp. 1–13.

    Google Scholar 

  58. E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge Univ. Press, Cambridge (2002).

    Google Scholar 

  59. E. B. Davies, “Markovian master equations,” Commun. Math. Phys., 39, 91–110 (1994).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. R. Courant and D. Hilbert, Methods of Mathematical Physics, New York (1953).

    MATH  Google Scholar 

  61. H. Barnum, C. M. Caves, C. Fuchs, R. Schack, D. J. Driebe, W. G. Hoover, H. Posch, B. L. Holian, R. Peierls, and J. L. Lebowitz, “Is Boltzmann entropy time’s arrow’s archer?” Phys. Today, 47, No. 11, 11–15 (1994).

    Article  ADS  Google Scholar 

  62. H. B. Callen, Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics, Wiley, New York (1960).

    MATH  Google Scholar 

  63. S. R. De Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, Amsterdam (1962).

    MATH  Google Scholar 

  64. L. Onsager, “Reciprocal relations in irreversible processes: I,” Phys. Rev., 37, 405–426 (1931).

    Article  ADS  MATH  Google Scholar 

  65. L. Onsager, “Reciprocal relations in irreversible processes: II,” Phys. Rev., 38, 2265–2279 (1931).

    Article  ADS  MATH  Google Scholar 

  66. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley-Interscience, New York (1971).

    MATH  Google Scholar 

  67. L. Tisza, “Concluding remarks,” in: Thermodynamics: History and Philosophy. Facts, Trends, Debates (K. Martinás, L. Ropolyi, and P. Szegedi, eds.), World Scientific, Singapore (1991), pp. 515–522.

    Google Scholar 

  68. C. Truesdell, Rational Thermodynamics, Springer, Berlin (1988).

    MATH  Google Scholar 

  69. D. Jou, J. Casas-Vázquez, and G. Lebon, Extended Irreversible Thermodynamics, Springer, Berlin (2010).

    Book  MATH  Google Scholar 

  70. D. Jou, J. Casas-Vázquez, and G. Lebon, “Extended irreversible thermodynamics,” Rep. Prog. Phys., 51, 1105–1179 (1988).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  71. G. Lebon, D. Jou, and J. Casas-Vázquez, “Questions and answers about a thermodynamic theory of the third type,” Contemp. Phys., 33, 41–51 (1992).

    Article  ADS  Google Scholar 

  72. G. Lebon and D. Jou, “Early history of extended irreversible thermodynamics (19532–1983): An exploration beyond local equilibrium and classical transport theory,” Eur. J. Phys. H, 40, 205–240 (2015).

    Article  Google Scholar 

  73. D. Jou, J. Casas-Vázquez, and G. Lebon, “Extended irreversible thermodynamics revisited,” Rep. Progr. Phys., 62, 1035–1142 (1999).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. I. Gyarmati, “On the wave appproach to thermodynamics and some problems of non-linear theories,” J. Non-Equilib. Thermodyn., 2, 233–260.

  75. M. Grmela, “Thermodynamics of driven systems,” Phys. Rev. E, 48, 919–930 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  76. N. Bernardes, “Thermodynamics and complementarity,” Phys. A, 260, 186–200 (1998).

    Article  Google Scholar 

  77. Á. R. Vasconcellos, R. Luzzi, and J. G. Ramos, “Irreversible thermodynamics in a nonequilibrium statisticalensemble formalism,” Riv. Nuovo Cimento, 24, 1–70 (2001).

    Google Scholar 

  78. R. Luzzi, Á. R. Vasconcellos, and J. G. Ramos, “The theory of irreversible processes: Foundations of a nonequilibrium statistical ensemble formalism,” Riv. Nuovo Cimento, 29, 1–82 (2006).

    Google Scholar 

  79. R. Luzzi, Á. R. Vasconcellos, and J. G. Ramos, “Non-equilibrium statistical mechanics of complex systems: An overview,” Riv. Nuovo Cimento, 30, 95–157 (2007).

    Google Scholar 

  80. C. A. B. Silva, J. G. Ramos, Á. R. Vasconcellos, and R. Luzzi, “Nonlinear higher-order hydrodynamics: Unification of kinetic and hydrodynamic approaches within a nonequilibrium statistical ensemble formalism,” arXiv:1210.7280v1 [physics.flu-dyn] (2012).

    Google Scholar 

  81. C. G. Rodrigues, Á. R. Vasconcellos, and R. Luzzi, “Mesoscopic hydro-thermodynamics of phonons in semiconductors: Heat transfer in III-nitrides,” Eur. Phys. J. B, 86, 200 (2013).

    Article  ADS  Google Scholar 

  82. Á. R. Vasconcellos, A. R. B. de Castro, C. A. B. Silva, and R. Luzzi, “Mesoscopic hydro-thermodynamics of phonons,” AIP Adv., 3, 072106–072133 (2013).

    Article  ADS  Google Scholar 

  83. C. A. B. Silva, C. G. Rodrigues, J. G. Ramos, and R. Luzzi, “Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism,” Phys. Rev. E, 91, 063011 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  84. C. G. Rodrigues, A. R. B. Castro, and R. Luzzi, “Higher-order generalized hydrodynamics of carriers and phonons in semiconductors in the presence of electric fields: Macro to nano,” Phys. Stat. Sol. B, 252, 2802–2819 (2015).

    Article  ADS  Google Scholar 

  85. C. G. Rodrigues, Á. R. Vasconcellos, and R. Luzzi, “Thermal conductivity in higher-order generalized hydrodynamics: Characterization of nanowires of silicon and gallium nitride,” Phys. E, 60, 50–58 (2014).

    Article  Google Scholar 

  86. J. L. del Río and L. S. García-Colín, “Repeated randomness assumption and the projection operator formalism,” Phys. Rev. E, 54, 950–953 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  87. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, Univ. Illinois Press, Urbana, Ill. (1949).

    MATH  Google Scholar 

  88. L. Brillouin, Science and Information Theory, Acad. Press, New York (1962).

    MATH  Google Scholar 

  89. I. Prigogine, Étude Thermodinamique des Phénomenès Irreversibles, Dover, Liège (1947).

    Google Scholar 

  90. S. A. Hassan, A. R. Vasconcellos, and R. Luzzi, “Informational-statistical thermodynamics of a dissipative system in a steady state,” Phys. A, 235, 345–368 (1997).

    Article  Google Scholar 

  91. E. T. Jaynes, “The evolution of Carnot’s principle,” in: Maximum Entropy and Bayesian Methods in Science and Engineering (G. J. Erickson and C. R. Smith, eds.), Kluwer, Dordrecht (1988), pp. 267–281.

    Chapter  Google Scholar 

  92. L. Rosenfeld, “On the foundations of statistical thermodynamics,” Acta Phys. Polon., 14, 3–29 (1955).

    MathSciNet  MATH  Google Scholar 

  93. L. Rosenfeld, “Questions on irreversibility and ergodicity,” in: Proc. Intl. School of Physics: “Enrico Fermi,” Course XIV (P. Caldirola, ed.), Acad. Press, New York (1960), pp. 1–20.

    Google Scholar 

  94. R. Luzzi, J. G. Ramos, and Á. R. Vasconcellos, “Rosenfeld–Prigogine complementarity of descriptions in the context of informational statistical thermodynamics,” Phys. Rev. E, 57, 244–251 (1998).

    Article  ADS  Google Scholar 

  95. E. T. Jaynes, Papers on Probability, Statistics, and Statistical Physics (Synth. Libr., Vol. 158), Reidel, Dordrecht (1983).

    Google Scholar 

  96. E. T. Jaynes, “Gibbs vs Boltzmann entropies,” Amer. J. Phys., 33, 391–399 (1965).

    Article  ADS  MATH  Google Scholar 

  97. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley-Interscience, New York (1977).

    MATH  Google Scholar 

  98. G. Nicolis, “Dissipative systems,” Rep. Progr. Phys., 49, 873–949 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  99. D. Jou and J. Casas-Vázquez, “Possible experiment to check the reality of a nonequilibrium temperature,” Phys. Rev. A, 45, 8371–8373 (1992).

    Article  ADS  Google Scholar 

  100. R. Luzzi, Á. R. Vasconcellos, J. Casas-Vázquez, and D. Jou, “On the selection of the state space in nonequilibrium thermodynamics,” Phys. A, 248, 111–137 (1998).

    Article  Google Scholar 

  101. R. Luzzi and Á. R. Vasconcellos, “Response function theory for far-from-equilibrium systems,” J. Statist. Phys., 23, 539–559 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  102. Á. R. Vasconcellos, R. Luzzi, D. Jou, and J. Casas-Vázquez, “Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach,” J. Chem. Phys., 107, 7383–7396 (1997).

    Article  ADS  Google Scholar 

  103. A. C. Algarte, Á. R. Vasconcellos, and R. Luzzi, “Kinetics of hot elementary excitations in photoexcited polar semiconductors,” Phys. Stat. Sol. B, 173, 487–514 (1992).

    Article  ADS  Google Scholar 

  104. A. C. Algarte, A. R. Vasconcellos, and R. Luzzi, “Ultrafast kinetics of evolution of optical phonons in a photoinjected highly excited plasma in semiconductors,” Phys. Rev. B, 54, 11311–11316 (1996).

    Article  ADS  Google Scholar 

  105. A. C. Algarte, A. R. Vasconcellos, and R. Luzzi, “Ultrafast phenomena in the photoinjected plasma in semiconductors,” Braz. J. Phys., 26, 543–552 (1996).

    ADS  Google Scholar 

  106. A. C. Algarte, A. R. Vasconcellos, and R. Luzzi, “Cooling of hot carriers in highly photoexcited semiconductors,” Phys. Rev. B, 38, 2162–2165 (1988).

    Article  ADS  Google Scholar 

  107. N. Bohr, “On the notions of causality and complementarity,” Dialectica, 2, 312–319 (1948).

    Article  MATH  Google Scholar 

  108. I. Prigogine, From Being To Becoming: Time and Complexity in the Physical Sciences, Freeman, San Francisco (1980).

    Google Scholar 

  109. H. Atlan, Entre le cristal et la fumèe: Essai sur l’organisation du vivant, Seuil, Paris (1986).

    Google Scholar 

  110. I. Prigogine and I. Stengers, Order Out Of Chaos, Bantam, New York (1984).

    Google Scholar 

  111. R. Landauer, “Information is physical,” Phys. Today, 44, No. 5, 23–31 (1991).

    Article  ADS  Google Scholar 

  112. S. J. Kline and N. Rosenberg, The Positive Sum Strategy: Harnessing Technology for Economic Growth, National Academy Press, Washington, DC (1986).

    Google Scholar 

  113. E. Lutz and S. Ciliberto, “Information: From Maxwell’s demon to Landauer’s eraser,” Phys. Today, 68, No. 9, 30–37 (2015).

    Article  Google Scholar 

  114. L. Szilard, “Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen,” Z. Physik, 53, 840–856 (1929).

    Article  ADS  MATH  Google Scholar 

  115. C. H. Bennett, “The thermodynamics of computation – a review,” Internat. J. Theor. Phys., 21, 905–940 (1982).

    Article  ADS  Google Scholar 

  116. L. Sklar, Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics, Cambridge Univ. Press, Cambridge (1993).

    Book  Google Scholar 

  117. J. Bricmont, D. Dürr, M. C. Galavotti, G. Ghirardi, F. Petruccione, and N. Zanghi, Chance in Physics: Foundations and Perspectives (Lect. Notes Phys., Vol. 574), Springer, Heidelberg (2001).

    Google Scholar 

  118. J. Bricmont, “Science of chaos or chaos in science?” Physicalia Magazine, 17, No. 32–4, 159–208 (1995).

    Google Scholar 

  119. J. Bricmont, “Science of chaos or chaos in science?” Ann. New York Acad. Sci., 775, 131–175 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  120. J. Meixner, “The entropy problem in thermodynamic processes,” Rheologica Acta, 12, 465–467 (1973).

    Article  Google Scholar 

  121. J. Meixner, “Entropy and entropy production,” in: Foundations of Continuum Thermodynamics (J. J. Delgado, M. N. Nina, and J. H. Whitelaw, eds.), MacMillan, London (1974), pp. 129–141.

    Google Scholar 

  122. J. Meixner and H. G. Reik, “Thermodynamik der irreversiblen Prozesse,” Handbuch der Physik, 3, 413–23 (1959).

    ADS  MathSciNet  Google Scholar 

  123. S. Abe and Y. Okamoto, eds., Nonextensive Statistical Mechanics and its Applications (Lect. Notes Phys., Vol. 560), Springer, Berlin (2001).

  124. J. N. Kapur and H. K. Kesavan, Entropy Optimization Principles with Applications, Acad. Press, Boston (1992).

    Book  MATH  Google Scholar 

  125. C. E. Shannon, “A mathematical theory of communication I,” Bell Syst. Tech. J., 27, 379–423 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  126. C. E. Shannon, “A mathematical theory of communication II,” Bell Syst. Tech. J., 27, 623–656 (1948).

    Article  MATH  Google Scholar 

  127. C. E. Shannon, Claude Elwood Shannon: Collected Papers (N. J. A. Sloane and A. D. Wyner, eds.), IEEE Press, New York (1993).

    MATH  Google Scholar 

  128. R. T. Cox, The Algebra of Probable Inference, The Johns Hopkins Univ. Press, Baltimore (1961).

    MATH  Google Scholar 

  129. A. Cho, “A fresh take on disorder, or disorderly science?” Science, 297, 1268–1269 (2002).

    Article  Google Scholar 

  130. R. Luzzi, Á. R. Vasconcellos, and J. G. Ramos, “Trying to make sense of disorder,” Science, 298, 1171–1172 (2002).

    Article  Google Scholar 

  131. R. Luzzi, Á. R. Vasconcellos, and J. G. Ramos, “Letter to the Editor: ‘On fallacies concerning nonextensive thermodynamics and q-entropy’,” Europhys. News, 37, No. 2, 11 (2006).

    Google Scholar 

  132. R. Balian and M. Nauenberg, “Letter to the Editor,” Europhys. News, 37, No. 2, 9 (2006).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Condensed Matter Physics Department, Institute of Physics “Gleb Wataghin,”, State University of Campinas-Unicamp, Campinas, Brazil

    R. Luzzi, A. R. Vasconcellos & J. G. Ramos

  2. Escola de Ciências Exatas e da Computação, Pontifícia Universidade Católica de Goiás, Goiânia, Goiás, Brazil

    C. G. Rodrigues

Authors
  1. R. Luzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. R. Vasconcellos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. G. Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. G. Rodrigues
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. G. Rodrigues.

Additional information

This research was supported in part by the São Paulo State Research Agency (FAPESP) and the Goiás State Research Agency (FAPEG).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 194, No. 1, pp. 7–38, January, 2018

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luzzi, R., Vasconcellos, A.R., Ramos, J.G. et al. Statistical Irreversible Thermodynamics in the Framework of Zubarev’s Nonequilibrium Statistical Operator Method. Theor Math Phys 194, 4–29 (2018). https://doi.org/10.1134/S0040577918010038

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577918010038

Keywords

Search

Navigation