Generalized information entropies in nonextensive quantum systems: The interpolation approach

TL;DR

This paper explores generalized entropy and Fisher information in nonextensive quantum systems using the interpolation approximation, analyzing their properties and numerical behavior in specific models.

Contribution

It introduces an analysis of generalized quantum entropies and Fisher information using the interpolation approximation, highlighting their metric properties and numerical results.

Findings

Interpolation approximation yields accurate quantal distributions.

Generalized Fisher information satisfies Cramér-Rao bounds.

Numerical results for electron and phonon models demonstrate the approach's effectiveness.

Abstract

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.