Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?

作者：Ran Guo; Du Jiulin^*

来源：Physica A: Statistical Mechanics and Its Applications , 2014, 406: 281-286.

DOI：10.1016/j.physa.2014.03.056

• Power-law distributions
• Detailed balance
• Generalized fluctuation-dissipation relation
• Nonequilibrium stationary-state

We examine whether the principle of detailed balance holds for the power-law distributions that are generated from the well-known two-variable Langevin equation and the associated Fokker-Planck equations. With the detailed balance and the generalized Fluctuation-dissipation relation, we derive analytically the stationary power-law distribution from the Ito's, Stratonovich's and Zwanzig's Fokker-Planck equations, and conclude that the power-law distributions can either be a stationary nonequilibrium distribution or an equilibrium distribution, which depend on information about the form of the diffusion coefficient function and the existence and uniqueness of an equilibrium state.

• 出版日期2014-7-15
• 单位天津大学