Variational Principle for the Pareto Power Law

Anirban Chakraborti (1, 2) , Patriarca Marco (3)

1 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
2 FiQuant - Chaire de finance quantitative
3 NICPB | KBFI - National Institute of Chemical Physics and Biophysics = Keemilise ja bioloogilise füüsika instituut [Estonie]

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Anirban Chakraborti, Patriarca Marco. Variational Principle for the Pareto Power Law. Physical Review Letters, 2009, 103 (22), pp.228701. ⟨10.1103/PhysRevLett.103.228701⟩. ⟨hal-00627629⟩