Tsallis统计量中状态总体对$q$值的敏感性及$q$的合理范围
The sensitivity of the population of states to the value of $q$ and the legitimate range of $q$ in Tsallis statistics
摘要：
在Tsallis统计力学的框架下，对自旋为1/2的谐振子，研究了当参数$q$变化时态布居的变化，结果表明，Boltzmann-Gibbs统计量和Tsallis统计量的预测结果之间的差异可以远远小于现有实验的精度.同时，重新研究了稀有/频繁事件特权与$q$值之间的关系。最后，在Tsallis统计力学的框架下，研究了一些简单模型系统配分函数的收敛准则，在此基础上，我们推测在热力学极限下，$q \leq 1$.
英文摘要：
In the framework of the Tsallis statistical mechanics, for the spin-1/2 and the harmonic oscillator, we study the change of the population of states when the parameter $q$ is varied; 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 the privilege of rare/frequent event and the value of $q$ is restudied. This relation is shown to be more complicated than the common belief about it. 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 $q \leq 1$, in the thermodynamic limit.
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