In the framework of the Tsallis statistical mechanics, we study the change of the population of states when the parameter q is varied, for some model systems; the results show that the difference between predictions of the Boltzmann-Gibbs and Tsallis statistics can be much smaller than the precision of any existing experiment. Also, the relation between privilege of rare and frequent events and the value of q is restudied. It is shown that positive q privilege frequent and negative q privilege rare events. Finally, the convergence criteria of the partition function of some simple model systems, in the framework of Tsallis statistical mechanics, is studied. Based on this study, we conjecture that q = 1, in the thermodynamic limit.

中文翻译：

---

Tsallis统计中的州人口对q值和q合法范围的敏感度

在Tsallis统计力学的框架中，对于某些模型系统，我们研究了当参数q改变时状态种群的变化。结果表明，Boltzmann-Gibbs预测与Tsallis统计之间的差异可能比任何现有实验的精度小得多。此外，还对罕见事件和频繁事件的特权与q值之间的关系进行了重新研究。结果表明，积极的q特权频繁事件和消极的q特权罕见事件。最后，在Tsallis统计力学的框架下，研究了一些简单模型系统的分区函数的收敛准则。根据这项研究，我们推测在热力学极限中q = 1。