Variational principle underlying scale invariant social systems

A. HERNANDO; A. PLASTINO

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

SPRINGER

Lugar: Berlin; Año: 2012 vol. 85 p. 293 - 301

1434-6028

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.