We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however which has no analogue for Shannon entropy, based on the notion of a Markov triangle, which may be thought of as a composition of communication channels for which conditional entropy acts functorially. Our proofs are coordinate-free in the sense that no logarithms appear in our calculations.

翻译：我们把相互信息描述为一对随机变量的独一无二的地图,这些随机变量符合一套与Faddeev对香农通则的特征相似的通则。 然而,我们的特性中有一个新的通则,根据Markov三角形的概念,它没有香农通则的类比,可被视为一种通信渠道的构成,而这种通信渠道是有条件的通则行为交织的。我们的证据是没有协调的,因为我们的计算中没有对数。