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

Citation
Ar. Lima et Tjp. Penna, Tsallis statistics with normalized q-expectation values is thermodynamically stable: illustrations, PHYS LETT A, 256(2-3), 1999, pp. 221-226
Citations number
8
Categorie Soggetti
Physics
Journal title
PHYSICS LETTERS A
ISSN journal
03759601 → ACNP
Volume
256
Issue
2-3
Year of publication
1999
Pages
221 - 226
Database
ISI
SICI code
0375-9601(19990531)256:2-3<221:TSWNQV>2.0.ZU;2-M
Abstract
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.