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 Kappa; (c) the associated Kappa-deformed entropy functional is obtained assuming the validity of H-Theorem in Kappa-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 Kappa 1, Kappa 2 controlling inhomogeneities in the directions x and y.(c) 2023 Elsevier B.V. All rights reserved.