Abstract
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.
Similar content being viewed by others
References
E.T. Jaynes, Phys. Rev. 106, 620 (1957)
E.T. Jaynes, Phys. Rev. 108, 171 (1957)
E.T. Jaynes, IEEE Trans. Syst. Sci. Cyb. 4, 227 (1968)
A. Katz, Principles of statistical mechanics: the information theory approach (W.H. Freeman, San Francisco, 1967)
M.E.J. Newman, Contemp. Phys. 46, 323 (2005)
S.K. Baek, S. Bernhardsson, P. Minnhagen, New J. Phys. 13, 043004 (2011)
H. Simon, Biometrika 42, 425 (1955)
B. Mandelbrot, Inform. Control 2, 90 (1959)
A. Hernando, D. Puigdomènech, D. Villuendas, C. Vesperinas, A. Plastino, Phys. Lett. A 374, 18 (2009)
A. Hernando, C. Vesperinas, A. Plastino, Physica A 389, 490 (2010)
A. Hernando, D. Villuendas, C. Vesperinas, M. Abad, A. Plastino, Eur. Phys. J. B 76, 87 (2010)
S.M. Ross, Introduction to Probability Models (Acadmic Press, NY, 2007)
F. Benford, Proc. Am. Philos. Soc. 78, 551 (1938)
E.W. Weisstein, “Benford’s Law”, From MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/BenfordsLaw.html
C. Tsallis, J. Stat. Phys. 52, 479 (1988)
C. Tsallis, Phys. Rev. E 58, 1442 (1998)
L. Zunino et al., Physica A 388, 1985 (2009)
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1965), Chap. 6.5
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hernando, A., Plastino, A. & Plastino, A.R. MaxEnt and dynamical information. Eur. Phys. J. B 85, 147 (2012). https://doi.org/10.1140/epjb/e2012-30009-3
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-30009-3