Tsallis Parameter Research Articles

Simulated annealing with Tsallis weights for a system of interacting hard spheres

In this paper we consider the Monte Carlo simulated annealings based on the Tsallis and threshold acceptance probabilities. This is done by applying them to the 2D system of many particles both interacting among themselves by a dipole–dipole potential and affected by the gravitational force. Our results confirm that for large and negative values of the Tsallis parameter q, the generalized method leads to low-energy configurations at higher temperatures, in fewer Monte Carlo steps and after shorter CPU time. We also suggest a qualitative explanation for them in terms of the acceptance probabilities used.

Q-boson system below the critical temperature

In this paper, we apply the q-algebra for a weakly interacting boson system. We find a physical example, a possible meaning and form for the q parameter of the algebra and we show its connection to the Tsallis parameter. We examine the behavior of this deformed boson gas below the critical temperature and we calculate the deformation of uncertainty relation in this region.

Tsallis entropy and the Vlasov-Poisson equations

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravitational N-body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following considerations we shall be dealing witha D-dimensional space so as to be in a position to investigate possible dimensional dependences of Tsallis' parameter q. The particular and important case of the Schuster solution is studied in detail, and the pertinent Tsallis parameter q is given as a function of the space dimension. In the special case of three dimensional space we recover the value q = 7/9, that has already appeared in many applications of Tsallis' formalism involving long range forces.

Experimental design for model discrimination of thermodynamic models

Traditionally, the screening of thermodynamic models in phase equilibria is performed only after obtaining a full set of experimental points. The aim of this work is to show that sequential model discrimination procedures may be used successfully to discriminate among rival thermodynamic models and thus, as a guide for more rational data collection. In order to do that, three different sequential experimental design procedures are implemented and used to model the solid–gas equilibrium at high pressures. One of the procedures is based on the Tsallis Statistics and depends on an empirical parameter which measures the risk that the experimenter is resolved to take in the decision-making stage. This procedure has been extended here to include prediction errors. It is shown here that the use of any of the three sequential discrimination procedures allow the selection of adequate models and model parameters with a significant reduction of the experimental effort. The Tsallis parameter is shown to exert a great influence upon the discarding of the models and the sequence of experiments. The prediction error is shown to be of fundamental importance for the proper selection of the next experiment.

A quantitative test of Gibbs' statistical mechanics

Tsallis' generalized statistical mechanics (GSM) is used in order to provide us with a test on the validity of the Gibbs-Boltzmann statistics, which constitutes a particular instance of the GSM, attained when the Tsallis parameter q equals unity. From both cosmic background data and the experimental value of the Stefan-Boltzmann constant, global and local bounds upon q are established.