Tsallis-Kaniadakis homotopy of position-dependent mass functions

We present a method for linking Tsallis and Kaniadakis statistics based on the concept of homotopy of curves. By homotopically connecting the position-dependent mass (PDM) functions from the Tsallis and Kaniadakis algebras, we generate a continuous family of homotopic PDM functions along with their associated homotopic canonical transformations. A homotopy family of Schrödinger equations associated to the homotopic PDM is presented. We work out the spectrum for the infinite well whose eigenfunctions are shown to manifest a mixture of inhomogeneities. The Kaniadakis and Tsallis cases are recovered for the homotopic parameter λ = 0 and λ = 1, respectively.