Generalized statistics variational perturbation approximation using q-deformed calculus

VENKATESAN, R.C.; A. PLASTINO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Año: 2010 vol. 389 p. 1159 - 1172

0378-4371

  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 HellmannFeynman 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-deformedqdeformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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-deformedq-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model vis- á-vis prior GVPA models are highlighted. 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 HellmannFeynman 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-deformedqdeformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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-deformedq-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.prior GVPA models are highlighted.q-deformed GVPA model vis- á-vis prior GVPA models are highlighted. 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 HellmannFeynman 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-deformedqdeformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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-deformedq-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.prior GVPA models are highlighted.prior GVPA models are highlighted. 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 HellmannFeynman 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-deformedqdeformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the HellmannFeynman 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-deformedq-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.q-deformed GVPA model vis- á-vis prior GVPA models are highlighted.prior GVPA models are highlighted.