Inhomogeneous Fokker–Planck equation from framework of Kaniadakis statistics

In this work we study an inhomogeneous Fokker–Planck equation (FPE) emerging in the framework of Kaniadakis statistics. The resultant FPE presents the features: (a) the solution is an special case of the Johnson’s SU-distribution as the response of the system to a delta form solicitation, (b) the mean standard deviation increases exponentially with a characteristic time depending on the deformation parameter κ; (c) the associated κ-deformed entropy functional is obtained assuming the validity of H-Theorem in κ-deformed space with the entropy contribution of the medium in terms of the deformation; and (d) the deformed derivatives carry the information about the inhomogeneities. Homogeneous diffusion is recovered in the limit of null deformation, and the results are generalized to the two-dimensional case with the presence of two deformation parameters κ1,κ2 controlling inhomogeneities in the directions x and y. •Inhomogeneous Fokker–Planck equation from master equation in kappa deformed space.•Exponential increasing diffusion with characteristic time depending on the deformation.•Kappa deformed entropy with contribution of the medium depending on the deformation.•Kappa deformed derivative carrying the information about the inhomogeneities.•Two dimensional case with two deformation parameters controlling the inhomogeneities.