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We examine whether the principle of detailed balance holds for the power-lawdistributions generated from the general Langevin equation under thegeneralized fluctuation-dissipation relation (FDR). With the detailed balanceand the generalized FDR, we derive analytically the stationary power-lawdistribution from the Ito's, Stratonovich's and Zwanzig's Fokker-Planckequations, and conclude that the power-law distributions can either be astationary nonequilibrium distribution or an equilibrium distribution, whichdepend on information about the form of the diffusion coefficient function, andthe existence and uniqueness of an equilibrium state.

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