q非可加性所隐含的关联使得q单原子气体具有高度的非平凡性
Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial
摘要：
众所周知，Tsallis的q-非可加性需要隐藏的相关性。它还表明，即使对于单原子气体，q-配分函数$Z$和平均能量$<U>$发散，特别是，表现出极的Tsallis非加性参数$q$的某些值。这是因为$Z$和$<U>$都依赖于$Γ$函数。该$Γ$又取决于空间维度$ν$。根据$Γ$ -函数的参数$A$，我们遇到三种不同的状态。(1)$A>0$，（2）极外的$A<0$和$Γ>0$。(3)$A$显示极点，通过维度正则化获得物理学。在情形（2）和（3）中，人们发现了引力效应和四分之一粒子。此外，束缚态和引力效应是隐藏的q关联的结果。
英文摘要：
It ts known that Tsallis' q-non-additivity entails hidden correlations. It has also been shown that even for a monoatomic gas, both the q-partition function $Z$ and the mean energy $<U>$ diverge and, in particular, exhibit poles for certain values of the Tsallis non additivity parameter $q$. This happens because $Z$ and $<U>$ both depend on a $Γ$-function. This $Γ$, in turn, depends upon the spatial dimension $ν$. We encounter three different regimes according to the argument $A$ of the $Γ$-function. (1) $A>0$, (2) $A<0$ and $Γ>0$ outside the poles. (3) $A$ displays poles and the physics is obtained via dimensional regularization. In cases (2) and (3) one discovers gravitational effects and quartets of particles. Moreover, bound states and gravitational effects emerge as a consequence of the hidden q-correlations.
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