Instability of q-expectation value
  q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general, whereas the ordinary expectation value is always stable. 
Sumiyoshi Abe (Mie University, Japan; ISMANS, Le Mans, France; Inspire   Institute Inc., Virginia, USA)