Tsallis statistics with normalized q-expectation values is thermodynamically stable: illustrations

We present a study of both the "Iterative Procedure" and the "beta --> beta ' transformation", proposed by Tsallis et al. (Physica A 261 (1998) 534) to find the probabilities p(i) of a system to be in a state with energy epsil on(i), within the framework of a generalized statistical mechanics. Using s tability and convexity arguments, we argue that the iterative procedure doe s not always provide the right temperature dependence of thermodynamic obse rvables. In addition, we show how to get the correct answers from the "beta --> beta' transformation". Our results provide an evidence that the Tsalli s statistics with normalized q-expectation values is stable for all ranges of temperatures. We also show that the cut-off in the computation of probab ilities is required to achieve the stable solutions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.