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Generalized Kinetic Equation for Far-from-Equilibrium Many-Body Systems

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Abstract

A kinetic equation for the single particle distribution function in an open many-body system, when in far away from equilibrium conditions is derived in the context of a Non-Equilibrium Thermo-Statistics of ample scope. It consists of a generalization of traditional kinetic equations in that no restrictions are imposed on the characteristics of the nonequilibrium thermodynamic state of the system. This kinetic equation do contain some contributions that become relevant in systems with a nonlinear kinetics when driven sufficiently far from equilibrium (certain complex systems). Moreover, the handling of the kinetic equation in a multiple-moment approach provides a generalized nonlinear higher-order thermo-hydrodynamics.

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References

  1. Akhiezer, A.I., Peletminskii, V.L.: Methods of Statistical Physics. Pergamon, Oxford (1981)

    Google Scholar 

  2. Algarte, A.C., Vasconcellos, A.R., Luzzi, R.: Kinetic of hot elementary excitations in photo excited polar semiconductors. Phys. Status Solidi (b) 173, 487 (1992)

    Article  ADS  Google Scholar 

  3. Alvarez-Romero, J.T., Garcia-Colin, L.S.: The foundations of informational statistical thermodynamics revisited. Physica A 232, 207 (1996)

    Article  ADS  Google Scholar 

  4. Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics. Wiley-Interscience, New York (1975)

    MATH  Google Scholar 

  5. Balian, R.: From Microphysics to Macrophysics, vol. 2. Springer, Berlin (2007)

    Google Scholar 

  6. Bogoliubov, N.N.: Lectures in Quantum Statistics I. Gordon & Breach, New York (1967)

    Google Scholar 

  7. Bogoliubov, N.N.: Lectures in Quantum Statistics II. Gordon & Breach, New York (1968)

    Google Scholar 

  8. Courant, R., Hilbert, D.: Methods of Mathematical Physics. Wiley-Interscience, New York (1953)

    Google Scholar 

  9. Duarte, O.S., Caldeira, A.O.: Effective coupling between two Brownian particles. Phys. Rev. Lett. 97, 250601 (2006)

    Article  ADS  Google Scholar 

  10. Family, F., Vicsek, T.: Dynamics of Fractal Surfaces. World Scientific, Singapore (1991)

    MATH  Google Scholar 

  11. Fano, U.: Description of states in quantum mechanics by density matrix and operator techniques. Rev. Mod. Phys. 29, 74 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Fonseca, A.F., Mesquita, M.V., Vasconcellos, A.R., Luzzi, R.: Informational-statistical thermodynamics of a complex system. J. Chem. Phys. 112, 3967 (2000)

    Article  ADS  Google Scholar 

  13. Gell-Mann, M., Goldberger, M.L.: The formal theory of scattering. Phys. Rev. 91, 398 (1953)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Grad, H.: On the kinetic theory of rarefied gasses. Commun. Pure Appl. Math. 2, 331 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  15. Grad, H.: Statistical mechanics, thermodynamics and fluid mechanics. Commun. Pure Appl. Math. 5, 455 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  16. Grad, H.: Principles of the kinetic theory of gases. In: Flügge, S. (ed.) Handbuch der Physik, vol. 12, pp. 205–294. Springer, Berlin (1958)

  17. Klimontovich, Yu.L.: Statistical Theory of Open Systems: A Unified Approach to Kinetic Description of Processes in Active Systems, vol. 1. Kluwer Academic, Dordrecht (1995)

    MATH  Google Scholar 

  18. Krylov, N.S.: Works on the Foundations of Statistical Mechanics. Princeton University Press, Princeton (1979)

    Google Scholar 

  19. Lauck, L., Vasconcellos, A.R., Luzzi, R.: A nonlinear quantum transport theory. Physica A 168, 789 (1990)

    Article  ADS  Google Scholar 

  20. Luzzi, R., Vasconcellos, A.R.: Ultrafast transient response of nonequilibrium plasma in semiconductors. In: Alfano, R.R. (ed.) Semiconductor Processes Probed by Ultrafast Laser Spectroscopy, vol. 1, pp. 135–169. Academic Press, New York (1984)

    Google Scholar 

  21. Luzzi, R., Vasconcellos, A.R., Ramos, J.G.: Predictive Statistical Mechanics: A Nonequilibrium Ensemble Formalism. Kluwer Academic, Dordrecht (2002)

    MATH  Google Scholar 

  22. Luzzi, R., Vasconcellos, A.R., Ramos, J.G.: The theory of irreversible processes: foundations of a non-equilibrium statistical ensemble formalism. Riv. Nuovo Cimento 29(2), 1 (2006)

    Google Scholar 

  23. Luzzi, R., Vasconcellos, A.R., Ramos, J.G.: Non-equilibrium statistical mechanics of complex systems: an overview. Riv. Nuovo Cimento 30(3), 95 (2007)

    Google Scholar 

  24. Madureira, J.R., Vasconcellos, A.R., Luzzi, R., Lauck, L.: Markovian kinetic equations in a nonequilibrium statistical ensemble formalism. Phys. Rev. E 57, 3637 (1998)

    Article  ADS  Google Scholar 

  25. Maxwell, J.C.: On the dynamical theory of gases. Philos. Trans. R. Soc. 157, 49 (1867)

    Article  Google Scholar 

  26. Mesquita, M.V., Vasconcellos, A.R., Luzzi, R.: Selective amplification of coherent polar vibrations in biopolymers. Phys. Rev. E 48, 4049 (1993)

    Article  ADS  Google Scholar 

  27. Mori, H.: Transport collective motion, and Brownian motion. Prog. Theor. Phys. 33, 423 (1965)

    Article  ADS  MATH  Google Scholar 

  28. Ramos, J.G., Vasconcellos, A.R., Luzzi, R.: A classical approach in predictive statistical mechanics: a generalized Boltzmann formalism. Fortschr. Phys./Prog. Phys. 43, 265 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Ramos, J.G., Vasconcellos, A.R., Luzzi, R.: A nonequilibrium ensemble formalism: criterium for truncation of description. J. Chem. Phys. 112, 2692 (2000)

    Article  ADS  Google Scholar 

  30. Ramos, J.G., Vasconcellos, A.R., Luzzi, R.: Derivation in a nonequilibrium ensemble formalism of a far reaching generalization of a quantum Boltzmann theory. Physica A 284, 140 (2000)

    Article  ADS  Google Scholar 

  31. Reif, R.: Foundations of Statistical and Thermal Physics. McGraw-Hill, New York (1965)

    Google Scholar 

  32. Rodrigues, C.G., Vasconcellos, A.R., Luzzi, R.: A kinetic theory for nonlinear quantum transport. Transp. Theory Stat. Phys. 29, 733 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Silva, C.A.B., Galvão, R.M.O.: Laser-assisted stopping power of a hot plasma for a system of correlated ions. Phys. Rev. E 60, 7435 (1999)

    Article  ADS  Google Scholar 

  34. Silva, C.A.B., Vasconcellos, A.R., Ramos, J.G., Luzzi, R.: Nonlinear higher-order hydrodynamics I. Unification of kinetic and hydrodynamic approaches within a nonequilibrium statistical ensemble formalism. Unpublished

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

    Book  Google Scholar 

  36. Spohn, H.: Kinetic equations from Hamiltonian dynamics: Markovian limits. Rev. Mod. Phys. 53, 569 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  37. Zubarev, D.N., Novikov, M.Yu.: Diagram method of construction of solutions of Bogolyubov’s chain of equations. Theor. Math. Phys. 9, 480 (1975)

    Google Scholar 

  38. Zubarev, D.N., Morosov, V.G., Röpke, G.: Statistical Mechanics of Nonequilibrium Processes, vols. 1 and 2. Akademie-Wiley VCH, Berlin (1996)

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Física, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP, Brazil

    C. A. B. Silva

  2. Condensed Matter Physics Department, Institute of Physics “Gleb Wataghin”, State University of Campinas—Unicamp, 13083-859, Campinas, SP, Brazil

    Aurea R. Vasconcellos, J. Galvão Ramos & Roberto Luzzi

Authors
  1. C. A. B. Silva
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  2. Aurea R. Vasconcellos
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  3. J. Galvão Ramos
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  4. Roberto Luzzi
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Corresponding author

Correspondence to C. A. B. Silva.

Additional information

The authors’ (A.R. Vasconcellos, J. Galvão Ramos, R. Luzzi) Home Page: www.ifi.unicamp.br/~aurea.

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Silva, C.A.B., Vasconcellos, A.R., Galvão Ramos, J. et al. Generalized Kinetic Equation for Far-from-Equilibrium Many-Body Systems. J Stat Phys 143, 1020–1034 (2011). https://doi.org/10.1007/s10955-011-0222-y

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  • DOI: https://doi.org/10.1007/s10955-011-0222-y

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