MaxEnt and dynamical information

  • A. Hernando
  • A. Plastino
  • A. R. Plastino
Regular Article


The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we show both theoretically and numerically that power laws and power laws with exponential cut-offs emerge as equilibrium densities in proportional and other dynamics.


Statistical and Nonlinear Physics 


  1. 1.
    E.T. Jaynes, Phys. Rev. 106, 620 (1957)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    E.T. Jaynes, Phys. Rev. 108, 171 (1957)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    E.T. Jaynes, IEEE Trans. Syst. Sci. Cyb. 4, 227 (1968)zbMATHCrossRefGoogle Scholar
  4. 4.
    A. Katz, Principles of statistical mechanics: the information theory approach (W.H. Freeman, San Francisco, 1967)Google Scholar
  5. 5.
    M.E.J. Newman, Contemp. Phys. 46, 323 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    S.K. Baek, S. Bernhardsson, P. Minnhagen, New J. Phys. 13, 043004 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    H. Simon, Biometrika 42, 425 (1955)MathSciNetzbMATHGoogle Scholar
  8. 8.
    B. Mandelbrot, Inform. Control 2, 90 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    A. Hernando, D. Puigdomènech, D. Villuendas, C. Vesperinas, A. Plastino, Phys. Lett. A 374, 18 (2009)ADSzbMATHCrossRefGoogle Scholar
  10. 10.
    A. Hernando, C. Vesperinas, A. Plastino, Physica A 389, 490 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    A. Hernando, D. Villuendas, C. Vesperinas, M. Abad, A. Plastino, Eur. Phys. J. B 76, 87 (2010)ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    S.M. Ross, Introduction to Probability Models (Acadmic Press, NY, 2007)Google Scholar
  13. 13.
    F. Benford, Proc. Am. Philos. Soc. 78, 551 (1938)Google Scholar
  14. 14.
    E.W. Weisstein, “Benford’s Law”, From MathWorld-A Wolfram Web Resource,
  15. 15.
    C. Tsallis, J. Stat. Phys. 52, 479 (1988)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    C. Tsallis, Phys. Rev. E 58, 1442 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    L. Zunino et al., Physica A 388, 1985 (2009)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1965), Chap. 6.5Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Laboratoire Collisions, Agrégats, Réactivité, IRSAMCUniversité Paul SabatierToulouse, Cedex 09France
  2. 2.Instituto Carlos I de Física Teórica y Computacional and Departamento de Física Atómica, Molecular y NuclearUniversidad de GranadaGranadaSpain
  3. 3.Physics Institute (IFLP-CCT-CONICET) C.C. 727National University La PlataLa PlataArgentina
  4. 4.CREG-National University La Plata-CONICET C.C. 727La PlataArgentina

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