We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined." Logical entropy provides that definition. Logical entropy is the natural measure of the notion of information based on distinctions, differences, distinguishability, and diversity. It is the (normalized) quantitative measure of the distinctions of a partition on a set--just as the Boole-Laplace logical probability is the normalized quantitative measure of the elements of a subset of a set. And partitions and subsets are mathematically dual concepts--so the logic of partitions is dual in that sense to the usual Boolean logic of subsets, and hence the name "logical entropy." The logical entropy of a partition has a simple interpretation as the probability that a distinction or dit (elements in different blocks) is obtained in two independent draws from the underlying set. The Shannon entropy is shown to also be based on this notion of information-as-distinctions; it is the average minimum number of binary partitions (bits) that need to be joined to make all the same distinctions of the given partition. Hence all the concepts of simple, joint, conditional, and mutual logical entropy can be transformed into the corresponding concepts of Shannon entropy by a uniform non-linear dit-bit transform. And finally logical entropy linearizes naturally to the corresponding quantum concept. The quantum logical entropy of an observable applied to a state is the probability that two different eigenvalues are obtained in two independent projective measurements of that observable on that state. Keywords: logical entropy, Shannon entropy, partitions, MaxEntropy, quantum logical entropy, von Neumann entropy

翻译：我们生活在信息时代。 Claude Shannon, 作为信息时代的父亲, 给了我们一个量化“信息数量数量”的通信理论, 但是, 正如他指出的那样, “信息本身没有定义概念本身。 ” 。 逻辑通则提供了该定义。 逻辑通则是基于区别、 差异、 区别和多样性的信息概念的自然度量。 这是( 标准化的) 数量量量度, 在一个设置上的分区, 因为 Boole- Laplace 逻辑概率是一组元素的子集元素的正常定量测量。 而分区和子集是数学意义上的双轨概念。 因此, 分区的逻辑在这种意义上是双轨的双轨概念。 因此, 偏差逻辑逻辑逻辑逻辑是“ 逻辑” 的自然度度度量。 分区的逻辑通则以两个独立方式获得分解( 不同区块的距离) 。 香农文则以信息分解的分母体的分数为基础, 分解的分母体的分母体, 直线将所有直径值都以两种直径为直径, 。