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Generalized statistics variational perturbation approximation using q-deformed calculus
Authors:RC Venkatesan  A Plastino
Institution:a Systems Research Corporation, Aundh, Pune 411007, India
b IFLP, National University La Plata & National Research Council (CONICET) C. C., 727 1900, La Plata, Argentina
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 q-deformed 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 vis-á-vis prior GVPA models are highlighted.
Keywords:Generalized Tsallis statistics  Additive duality  Variational perturbation approximations  q-deformed calculus  Hellmann-Feynman theorem  Generalized Bogoliubov inequality
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