Tsallis' statistics for long range interactions: gravity

Abstract

Using Schwartz’ distribution-theory tools developed in Plastino and Rocca (2018) and applied in several recent references we compare the canonical ensemble treatment of gravity for both Boltzmann–Gibbs’ and Tsallis’ statistics. We provide new arguments, based on the celebrated Cramer Rao inequality, supporting the long dated conjecture that Tsallis statistics is the proper one for dealing with long range interactions.