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

• DOI: 10.1016/j.physa.2014.03.056
• Publication Date: 2014-03-27T13:36:24Z
• Authors: Ran Guo; Jiulin Du
• Keywords: Detailed balance; Stationary distribution; Stationary state; Langevin equation

We examine whether the principle of detailed balance holds for the power-law distributions generated from the general Langevin equation under the generalized fluctuation-dissipation relation (FDR). With the detailed balance and the generalized FDR, 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.<br/>9 pages, 39 references<br/>