On a 2-relative entropy

James Fullwood

doi:10.3390/e24010074

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arXiv · 2112.03582

On a 2-relative entropy

James Fullwood

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Abstract

We construct a 2-categorical extension of the relative entropy functor of Baez and Fritz, and show that our construction is functorial with respect to vertical morphisms. Moreover, we show such a `2-relative entropy' satisfies natural 2-categorial analogues of convex linearity, vanishing under optimal hypotheses, and lower semicontinuity. While relative entropy is a relative measure of information between probability distributions, we view our construction as a relative measure of information between channels.

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James Fullwood. 2021-12-07. On a 2-relative entropy. https://doi.org/10.3390/e24010074

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