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arXiv · 2306.02412

Generalised Br\`{e}gman relative entropies: a brief introduction

Ryszard Paweł Kostecki
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Abstract

We present some basic elements of the theory of generalised Br\`{e}gman relative entropies over nonreflexive Banach spaces. Using nonlinear embeddings of Banach spaces together with the Euler--Legendre functions, this approach unifies two former approaches to Br\`{e}gman relative entropy: one based on reflexive Banach spaces, another based on differential geometry. This construction allows to extend Br\`{e}gman relative entropies, and related geometric and operator structures, to arbitrary-dimensional state spaces of probability, quantum, and postquantum theory. We give several examples, not considered previously in the literature.

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Ryszard Paweł Kostecki. 2023-06-04. Generalised Br\`{e}gman relative entropies: a brief introduction. https://arxiv.org/abs/2306.02412

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