title: Variational principle for the Pareto power law.
abstract: A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system.
authors.affiliation: Laboratoire de Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, 92290 Châtenay-Malabry, France. anirban.chakraborti@ecp.fr
authors.forename: Anirban
authors.initials: A
authors.lastname: Chakraborti
authors.forename: Marco
authors.initials: M
authors.lastname: Patriarca