Generalized information entropies in nonextensive quantum systems: The interpolation approach

Details Generalized information entropies in nonextensive quantum systems: The interpolation approach Generalized information entropies in nonextensive quantum systems: The interpolation approach

2009-09-20

arxiv.org/abs/0909.3620v1

Physics

Condensed Matter

Statistical Mechanics

19 pages, 8 figures

Scientific paper

We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal distributions within $O(q-1)$ and in high- and low-temperature limits, $q$ being the entropic index [H. Hasegawa, Phys. Rev. E 80 (2009) 011126]. Three types of GFIs which have been proposed so far in the nonextensive statistics, are discussed from the viewpoint of their metric properties and the Cram\'{e}r-Rao theorem. Numerical calculations of the $q$- and temperature-dependent Tsallis entropy and GFIs are performed for the electron band model and the Debye phonon model.

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