Variational principle for the Pareto power law
Anirban Chakraborti, Marco Patriarca
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.
Create a lesson
Related papers
Long-time Dynamics of Many-body Open Quantum Systems using Quantum Generating Functions
Katha Ganguly, Dario Poletti, Bijay Kumar Agarwalla
Localization Delocalization Transition in Diffusion with Adaptive Resetting
Tommer D. Keidar, Shlomi Reuveni
Quenched activity induces nonuniversal scaling in nonreciprocal XY Models and surfaces
Sudip Mukherjee, Abhik Basu
Brownian yet non-Gaussian diffusion through equilibrium nonlinear friction
Jakob Mihatsch, Andreas M. Menzel
When dissipative steady states admit thermodynamic occupation laws
Tetsu Ichitsubo
Fluctuation--response relations from an emergent Z2 symmetry in the rotating stochastic Landau model
Dhruv Kush, Nicki Mullins, Mauricio Hippert et al.