Deformed random walk: Suppression of randomness and inhomogeneous diffusion.

We study a generalization of the random walk (RW) based on a deformed translation of the unitary step, inherited by the q algebra, a mathematical structure underlying nonextensive statistics. The RW with deformed step implies an associated deformed random walk (DRW) provided with a deformed Pascal triangle along with an inhomogeneous diffusion. The paths of the RW in deformed space are divergent, while those corresponding to the DRW converge to a fixed point.

Reply to "Comment on 'Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass"'.

It is shown that in the "Comment on 'Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass,"' three crucial observations have gone unnoticed, thus restricting its conclusion on the legitimacy of the Langevin equation for a position-dependent mass, Eq. (46) of da Costa et al. [Phys.

Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass.

We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space where the linear (nonlinear) character of the FPE is associated with the employed deformed linear (nonlinear) derivative. The FPE for an inhomogeneous medium with a position-dependent diffusion coefficient is equivalent to a deformed FPE within a deformed space, described by generalized derivatives, and constant diffusion coefficient. The deformed FPE is consistent with the diffusion equation for inhomogeneous media when the temperature and the mobility have the same position-dependent functional form as well as with the nonlinear Langevin approach.

Majorization and Dynamics of Continuous Distributions.

In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the -Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions ϕ for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker-Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements.

Distinguishability notion based on Wootters statistical distance: Application to discrete maps.

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d¯ for an arbitrary discrete map.