论文标题
在广义统计力学的背景下，杰克逊和豪斯多夫衍生物之间的联系
The connection between Jackson and Hausdorff derivatives in the context of generalized statistical mechanics
论文作者
论文摘要
在文献中，人们可以发现常规莱布尼兹衍生物的许多概括，例如杰克逊衍生物，tsallis衍生物和豪斯多夫衍生物。在本文中，我们介绍了杰克逊衍生物与最近提出的Hausdorff衍生产品之间的联系。一方面，Hausdorff衍生物先前与呈现分形方面的系统中的非扩展性相关。另一方面，杰克逊衍生物具有坚实的数学基础，因为它是普通导数的$ \叠加{q} $ - 类似物，并且也出现在Quantum conculus中。从量子变形的$ \叠加{q} $ - 代数我们获得杰克逊衍生物，然后解决$ n $ noteracting量子振荡器的问题。我们在量子宏伟的分区函数中进行扩展，从中，我们从中获得了与杰克逊衍生产品有关的参数$ \ overline {q} $，而参数$ζ$和$ q $分别与Hausdorff衍生产品和tsallis衍生物有关。
In literature one can find many generalizations of the usual Leibniz derivative, such as Jackson derivative, Tsallis derivative and Hausdorff derivative. In this article we present a connection between Jackson derivative and recently proposed Hausdorff derivative. On one hand, the Hausdorff derivative has been previously associated with non-extensivity in systems presenting fractal aspects. On the other hand, the Jackson derivative has a solid mathematical basis because it is the $\overline{q}$-analog of the ordinary derivative and it also arises in quantum calculus. From a quantum deformed $\overline{q}$-algebra we obtain the Jackson derivative and then address the problem of $N$ non-interacting quantum oscillators. We perform an expansion in the quantum grand partition function from which we obtain a relationship between the parameter $\overline{q}$, related to Jackson derivative, and the parameters $ζ$ and $q$ related to Hausdorff derivative and Tsallis derivative, respectively.
