Instability of q-averages in nonextensive statistical mechanicsS. Abe
Department of Physical Engineering, Mie University - Mie 514-8507, Japan
received 21 June 2008; accepted in final form 21 November 2008; published December 2008
published online 12 January 2009
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.
02.50.Cw - Probability theory.
05.20.-y - Classical statistical mechanics.
05.90.+m - Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems.
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