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

Abstract

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.

9 pages, 39 references

References in corpus (5)

• Relativistic Brownian Motion
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Thermostatistics of overdamped motion of interacting particles
• Kramers escape rate in overdamped systems with the power-law distribution
• Acoustic Kappa-Density Fluctuation Waves in Suprathermal Kappa Function Fluids

Cited by in corpus (5)

• The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion
• Thermodynamics aspects of noise-induced phase synchronization
• Dynamic of Stochastic Gradient Descent with State-Dependent Noise
• Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations
• The collisional relaxation rate of kappa-distributed plasma with multiple components