Generalized statistics variational perturbation approximation using q-deformed calculus

Abstract

A principled framework to generalize variational perturbation approximations (VPAs) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free energy (GFE) with a variational procedure formulated using qdeformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the Hellmann–Feynman theorem. The generalized Bogoliubov inequality for the approximate GFE are derived for the case of canonical probability densities that maximize the Tsallis entropy. Numerical examples demonstrating the application of the q-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model visá-vis prior GVPA models are highlighted.