论文标题
更改有条件熵的系数
Change the coefficients of conditional entropies in extensivity
论文作者
论文摘要
Boltzmann - gibbs熵是对概率度量空间的功能。当一个状态空间可数时，玻尔兹曼（Gibbs）熵的一个表征由香农 - khinchin Axioms给出，该公理由连续性，最大性，可扩展性和扩展性组成。在这四个属性中，扩展性以各种方式概括。功能的扩展性被解释为对任何随机变量$（x，y）$的属性，在$ \ mathbb {n} $中有限的值有限的值，在$（x，y）$的联合定律中，功能的差额与$ x $的概率$ y $ y $ y $ x y $ x $ x = y $ x =每个事件$ x = n $。通过用事件概率$ x = n $替换系数的功能，获得的扩展性的概括提供了Tsallis熵的表征。 在本文中，我们首先证明不可能用事件概率的非功率函数替换系数$ x = n $。然后，我们估计$（x，y）$的联合法律的价值与一般功能的$ x $法律之间的差异。
The Boltzmann--Gibbs entropy is a functional on the space of probability measures. When a state space is countable, one characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity, maximality, expandability and extensivity. Among these four properties, the extensivity is generalized in various ways. The extensivity of a functional is interpreted as the property that, for any random variables $(X,Y)$ taking finitely many values in $\mathbb{N}$, the difference between the value of the functional at the joint law of $(X,Y)$ and that at the law of $X$ coincides with the linear combinations of the values at the conditional laws of $Y$ given $X=n$ with coefficients given by the probabilities of each event $X=n$. A generalization of the extensivity obtained by replacing the coefficients with a power of the probabilities of the events $X=n$ provides a characterization of the Tsallis entropy. In this paper, we first prove the impossibility to replace the coefficients with a non-power function of the probabilities of the events $X=n$. Then we estimate the difference between the value at the joint law of $(X,Y)$ and that at the law of $X$ for a general functional.
