Issue
EPL
Volume 84, Number 6, December 2008
Article Number 60006
Number of page(s) 3
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/60006
Published online 12 January 2009
EPL, 84 (2008) 60006
DOI: 10.1209/0295-5075/84/60006

Instability of q-averages in nonextensive statistical mechanics

S. Abe

Department of Physical Engineering, Mie University - Mie 514-8507, Japan

suabe@sf6.so-net.ne.jp

received 21 June 2008; accepted in final form 21 November 2008; published December 2008
published online 12 January 2009

Abstract
A generalization of the definition of average value of a physical quantity has been discussed in the literature. In particular, the so-called q-average is widely used in the field of nonextensive statistical mechanics. Here, it is shown that the q-average is not stable under small deformations of a probability distribution function, in general, whereas the normal average is always stable.

PACS
02.50.Cw - Probability theory.
05.20.-y - Classical statistical mechanics.
05.90.+m - Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems.

© EPLA 2008