https://doi.org/10.1140/epjb/e2012-30313-x
Regular Article
Variational principle underlying scale invariant social systems
1 Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 09, France
2 National University La Plata, IFLP-CCT-CONICET, C.C. 727, 1900 La Plata, Argentina
3 Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca, Spain
a
e-mail: alberto.hernando@irsamc.ups-tlse.fr
Received: 11 April 2012
Received in final form: 8 June 2012
Published online: 29 August 2012
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012
