1202.0707 (Du Jiulin)

Power-law distributions and fluctuation-dissipation relation in the
stochastic dynamics of two-variable Langevin equations    [PDF]

Du Jiulin

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.

View original: http://arxiv.org/abs/1202.0707