Statistical treatment of autonomous systems with divergencelless flows

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Abstract

Statistical Mechanics (SM) has been quite successful in providing one with exact, or at least approximate, descriptions of the time-dependent solutions of the Liouville (or of the von Neumann) equation within the context of Hamiltonian dynamics (HD). Here we investigate how to extend some of its ideas to more general dynamical systems. We find that for systems that retain from HD just the divergenceless character of the phase space flow many ideas borrowed from the Maximum Entropy Principle approach to SM apply in such a generalized context as well.

References (47)

  • L. Andrey

    Phys. Lett. A

    (1985)
  • W.-H. Steeb

    Physica A

    (1979)
  • L. Andrey

    Phys. Lett. A

    (1986)
  • J. Ramshaw

    Phys. Lett. A

    (1986)
  • E. Kerner

    Phys. Lett. A

    (1990)
  • I. Bialynicki-Birula et al.

    Phys. Lett. A

    (1991)
  • R. Balian et al.

    Ann. Phys.

    (1985)
  • R. Levine et al.

    Nucl. Phys. A

    (1986)
  • R. Balian et al.

    Ann. Phys.

    (1987)
  • R. Balian et al.

    Ann. Phys.

    (1988)
  • D. Napoli et al.

    Nucl. Phys. A

    (1989)
  • N. Canosa et al.

    Nucl. Phys. A

    (1990)
  • N. Canosa et al.

    Nucl. Phys. A

    (1992)
  • A.R. Plastino et al.

    Phys. Lett. A

    (1993)
  • H. Varela et al.

    Physica A

    (1994)
  • A.R. Plastino et al.

    Physica A

    (1994)
  • S. Smale
  • J. Liouville

    J. Math. Pure Appl.

    (1838)
  • Y. Nambu

    Phys. Rev. D

    (1973)
  • J. Jaynes

    Phys. Rev.

    (1957)
  • J. Jaynes

    Phys. Rev.

    (1957)
  • L. Brillouin

    Science and Information Theory

    (1956)
  • A. Katz

    Principles of Statistical Mechanics

    (1967)
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