Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-02-03
J. Stat. Mech.(2012)P02006
Physics
Condensed Matter
Statistical Mechanics
18 pages,63 references
Scientific paper
10.1088/1742-5468/2012/02/P02006
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a condition under which these power-law distributions are accurately created in a system away from equilibrium. This condition is an energy-dependent relation between the diffusion coefficient and the friction coefficient and thus it provides a fluctuation-dissipation relation for nonequilibrium systems with power-law distributions. Further, we study the specific forms of the Fokker-Planck equation that correctly leads to such power-law distributions, and then present a possible generalization of Klein-Kramers equation and Smoluchowski equation to a complex system, whose stationary-state solutions are exactly a Tsallis distribution.
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