论熵的线性组合与极值分布的线性组合之间的联系
On the connection between linear combination of entropies and linear combination of extremizing distributions
摘要：
我们分析的分布，极值玻尔兹曼-吉布斯熵和非添加剂$q$ -熵的线性组合。我们表明，这种分布可以表示在一个朗伯函数。熵泛函和极值分布都可以与一个非线性Fokker-Planck方程相联系，该方程是由具有非线性跃迁速率的主方程得到的。此外，我们评估由高斯分布（使玻尔兹曼-吉布斯熵极值化）和$q$ -高斯分布（使$q$ -熵极值化）的线性组合极值化的熵。我们给出了$q=0$的显式表达式，并对其它情况进行了数值讨论.对于$q=0$，我们得到的熵可以用朗伯函数表示，并且对于$q<1$的所有值，在二阶导数中表现出不连续性。整个讨论是密切相关的第二类超导体和标准地图的统计最近的结果。
英文摘要：
We analyze the distribution that extremizes a linear combination of the Boltzmann--Gibbs entropy and the nonadditive $q$-entropy. We show that this distribution can be expressed in terms of a Lambert function. Both the entropic functional and the extremizing distribution can be associated with a nonlinear Fokker--Planck equation obtained from a master equation with nonlinear transition rates. Also, we evaluate the entropy extremized by a linear combination of a Gaussian distribution (which extremizes the Boltzmann--Gibbs entropy) and a $q$-Gaussian distribution (which extremizes the $q$-entropy). We give its explicit expression for $q=0$, and discuss the other cases numerically. The entropy that we obtain can be expressed, for $q=0$, in terms of Lambert functions, and exhibits a discontinuity in the second derivative for all values of $q<1$. The entire discussion is closely related to recent results for type-II superconductors and for the statistics of the standard map.
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