标题： 广义熵的微观解释 显示英文标题

标题： Microscopic interpretation of generalized entropy

摘要： 广义熵最近被提出，它将所有已知的看似不同的熵，如Tsallis熵、Rényi熵、Barrow熵、Kaniadakis熵、Sharma-Mittal熵以及环量子引力熵置于一个统一的框架下。 然而，这种广义熵的微观起源及其与热力学系统的关系尚不明确。 在本工作中，我们将从正则系综和巨正则系综的角度提供对广义熵的微观热力学解释。 结果表明，在正则系综和巨正则系综的描述中，广义熵可以被解释为一系列微观量的统计系综平均值，这些微观量由$\left(-k\ln{\rho}\right)^n$的不同幂次给出（其中$n$是一个正整数，$\rho$表示相应系综的相空间密度），同时还包括一个代表所考虑系统哈密顿量和粒子数涨落的项（在正则系综的情况下，粒子数的涨落消失）。 显示英文摘要

摘要： Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the R\'{e}nyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single umbrella. However, the microscopic origin of such generalized entropy as well as its relation to thermodynamic system(s) is not clear. In the present work, we will provide a microscopic thermodynamic explanation of generalized entropy(ies) from canonical and grand-canonical ensembles. It turns out that in both the canonical and grand-canonical descriptions, the generalized entropies can be interpreted as the statistical ensemble average of a series of microscopic quantity(ies) given by various powers of $\left(-k\ln{\rho}\right)^n$ (with $n$ being a positive integer and $\rho$ symbolizes the phase space density of the respective ensemble), along with a term representing the fluctuation of Hamiltonian and number of particles of the system under consideration (in case of canonical ensemble, the fluctuation on the particle number vanishes).