Fluctuations and Power Low Distribution Function in Nonequilibrium Systems

The Fokker–Planck equation is formulated for the distribution functions of macroscopic open systems in the space of slowly changing physical variables (energy, adiabatic invariants, etc.). The stationary solution of such equations determines a quasi-equilibrium distribution function in the relevant space. The proposed approach involves the evolution of systems under the action of dissipation and diffusion in the space of the appropriate variables. It is shown that the well-known power law distribution can be obtained by considering internal and external fluctuations in statistical systems.