一种基于群论结构的新熵
A new entropy based on a group-theoretical structure
摘要：
介绍了非加性熵的多参数版本$S_{q}$。这种新的熵形式，记为$S_{a,b,r}$，具有许多有趣的统计性质，它简化为$b=0$的熵$S_q$，$a=r:=1-q$（因此是$b=0$的玻尔兹曼-吉布斯熵$S_{BG}$，$a=r \to 0$）。熵$S_{a,b,r}$的构建是基于我们之一\cite{Tempesta2}最近提出的一般群论方法。事实上，这个新熵的所有性质基本上都是由于存在一个有理群律而得到的，该群律表达了$S_{a,b,r}$相对于统计独立子系统的组成的结构。取决于参数的选择，熵$S_{a,b,r}$可用于覆盖广泛的物理情况，其中可访问相空间的测量随着系统的粒子数$N$呈指数增加，或者甚至通过将$N$增加到极限值而稳定。这为在系统通过增加其组成粒子或子系统的数量来“冻结”其部分或多个自由度的情况下使用这种熵铺平了道路。
英文摘要：
A multi-parametric version of the nonadditive entropy $S_{q}$ is introduced. This new entropic form, denoted by $S_{a,b,r}$, possesses many interesting statistical properties, and it reduces to the entropy $S_q$ for $b=0$, $a=r:=1-q$ (hence Boltzmann-Gibbs entropy $S_{BG}$ for $b=0$, $a=r \to 0$). The construction of the entropy $S_{a,b,r}$ is based on a general group-theoretical approach recently proposed by one of us \cite{Tempesta2}. Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of $S_{a,b,r}$ with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy $S_{a,b,r}$ can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles $N$ of the system, or even stabilizes, by increasing $N$, to a limiting value. This paves the way to the use of this entropy in contexts where a system "freezes" some or many of its degrees of freedom by increasing the number of its constituting particles or subsystems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
