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

Abstract

We present a study of both the ``Iterative Procedure'' and the ``$\beta \to {\beta }^{\prime }$ transformation'', proposed by Tsallis et al (Physica A261, 534) to find the probabilities $p_i$ of a system to be in a state with energy ${\epsilon }_i$, within the framework of a generalized statistical mechanics. Using stability and convexity arguments, we argue that the iterative procedure does not always provide the right temperature dependence of thermodynamic observables. In addition, we show how to get the correct answers from the ``$\beta \to {\beta }^{\prime }$ transformation''. Our results provide an evidence that the Tsallis statistics with normalized q-expectation values is stable for all ranges of temperatures. We also show that the cut-off in the computation of probabilities is required to achieve the stable solutions.

8 pages, 5 figures, elsevier preprint format (requires elsart.cls). Submitted to Phys. Lett. A

References in corpus (1)

• Monte Carlo Simulation of Magnetic System in the Tsallis Statistics

Cited by in corpus (11)

• Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis
• Magnetic phase diagram for a non-extensive system: Experimental connection with manganites
• Magnetic behavior of a non-extensive S-spin system: possible connections to manganites
• A non self-referential expression of Tsallis' probability distribution function
• A Comment on the Tsallis Maximum Entropy Principle
• Thermostatistics of extensive and non-extensive systems using generalized entropies
• Majorization properties of generalized thermal distributions
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• A Monte Carlo Method for the Numerical Simulation of Tsallis Statistics
• Polygamy of multi-party $q$-expected quantum entanglement
• Ising model in the Rényi statistics: the finite size effects