Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving *-homomorphisms to real numbers. Our axioms reproduce those of Baez, Fritz, and Leinster characterizing the Shannon entropy difference. The existence of disintegrations for classical probability spaces plays a crucial role in our characterization.

翻译：使用康韦克斯·格罗芬迪克的纤维化,我们把冯·诺伊曼(von Neumann entropy)描述为从有限维度的非混合概率空间和州保护的异形主义到真实数字的杀菌剂。 我们的原教旨复制了Baez、Fritz和Leinster(香农的分泌差异)的特性。 古典概率空间的分解在我们的特征定性中起着关键作用。