Variational principle underlying scale invariant social systems

Regular Article

DOI: 10.1140/epjb/e2012-30313-x

Cite this article as:
Hernando, A. & Plastino, A. Eur. Phys. J. B (2012) 85: 293. doi:10.1140/epjb/e2012-30313-x


MaxEnt’s variational principle, in conjunction with Shannon’s logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the incorporation, into the variational process, of suitable dynamical information. As a consequence, we are able to formulate a somewhat generalized Shannonian maximum entropy approach which provides a unifying “thermodynamic-like” explanation for the scale-invariant phenomena observed in social contexts, as city-population distributions. We confirm the MaxEnt predictions by means of numerical experiments with random walkers, and compare them with some empirical data.


Statistical and Nonlinear Physics 

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.IFLP-CCT-CONICETNational University La PlataLa PlataArgentina
  3. 3.Universitat de les Illes Balears and IFISC-CSICPalma de MallorcaSpain

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