Generalized statistics variational perturbation approximation using q-deformed calculus

R.C. Venkatesan and A. Plastino

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 6, 1159-1172

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 (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:6:p:1159-1172

DOI: 10.1016/j.physa.2009.11.033

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