Department of Physics, School of Science and Technology, Nazarbayev University, Astana 010000, Kazakhstan.
Department of Materials Science and Nanotechnology Engineering, TOBB University of Economics and Technology, 06560 Ankara, Turkey.
Phys Rev E. 2018 Jan;97(1-1):012104. doi: 10.1103/PhysRevE.97.012104.
The existence and exact form of the continuum expression of the discrete nonlogarithmic q-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic q-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic q-entropy in fact converges in the continuous limit and the negative of the q-entropy with continuous variables is demonstrated to lead to the (Csiszár type) q-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the q-entropy to the continuous classical physical systems.
离散非对数 q-熵的连续表达式的存在和确切形式是广义统计力学中的一个重要未解决问题，因为其可能的缺失意味着非对数 q-熵与连续经典系统无关。在这项工作中，我们展示了离散非对数 q-熵实际上是如何在连续极限中收敛的，并且证明了具有连续变量的 q-熵导致（Csiszár 型）q-相对熵，就像连续的玻尔兹曼-吉布斯表达式与 Kullback-Leibler 相对熵之间的关系一样。因此，我们得出结论，q-熵在连续经典物理系统中的应用没有障碍。
