Generalised Br\`{e}gman relative entropies: a brief introduction
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.
Cite
@article{arxiv.2306.02412,
title = {Generalised Br\`{e}gman relative entropies: a brief introduction},
author = {Ryszard Paweł Kostecki},
journal= {arXiv preprint arXiv:2306.02412},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:1710.01837 (author's note: this overlap will be removed in the upcoming v5 of arXiv:1710.01837 and the upcoming v4 of this paper); v3: minor change (grant numbers)