Transport Equation for Small Systems and Nonadditive Entropy

Abstract: The nonadditive entropy introduced by Tsallis in 1988 has been used in different fields and generalizes the Boltzmann entropy extending the possibilities of application of the statistical methods developed in the context of Mechanics. Here we investigate one of the last points of the theory that still are under discussion: the source term of the nonextensive transport equation. Based on a simple system, we show that the nonadditivity is a direct consequence of the phase space topology, and derive the source term that leads to the nonextensive transport equation.