We consider a multifractal structure as a mixture of fractal substructures and introduce a distribution function f (α), where α is a fractal dimension. Then we can introduce g(p) ∼ µ − ln p e −y f (y)dy and show that the distribution functions f (α) in the form of f (α) = δ (α − 1), f (α) = δ (α − θ), f (α) = 1 α−1 , f (y) = y α−1 lead to the Boltzmann-Gibbs, Shafee, Tsallis and Anteneodo-Plastino entropies conformably. Here δ (x) is the Dirac delta function. Therefore the Shafee entropy corresponds to a fractal structure, the Tsallis entropy describes a multifractal structure with a homogeneous distribution of fractal substructures and the Anteneodo-Plastino entropy appears in case of a power law distribution f (y). We consider the Fokker-Planck equation for a fractal substructure and determine its stationary solution. To determine the distribution function of a multifractal structure we solve the twodimensional Fokker-Planck equation and obtain its stationary solution. Then applying the Bayes theorem we obtain a distribution function for the entire system in the form of q-exponential function. We compare the results of the distribution functions obtained due to the superstatistical approach with the ones obtained according to the maximum entropy principle.
It is shown in a phenomenological approach that the symmetry space group I4/mmm of the paramagnetic phase in compounds of the ThCr2Si2 type arises as a result of a structural phase transition from a close-packed paraphase with space group Im3m. It is found that the real magnetic orderings in compounds of the ThCr2Si2 type is described by transition parameters belonging to a single direction, along the line joining the points of maximum symmetry in the Brillouin zone of the I4/mmm group. It is shown that the variations of the modulus of the wave vector are a consequence of a change in the dopant concentration. The spatial dependence of the order parameter in the incommensurate phases is obtained for the corresponding universality classes.
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