Variational principle for the Pareto power law

Details Variational principle for the Pareto power law Variational principle for the Pareto power law

2006-05-12

arxiv.org/abs/cond-mat/0605325v3

Physics

Condensed Matter

Statistical Mechanics

Revised version, 4 pages and 1 figure

Scientific paper

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.

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