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We present some basic elements of the theory of generalised Br\`{e}gmanrelative entropies over nonreflexive Banach spaces. Using nonlinear embeddingsof Banach spaces together with the Euler--Legendre functions, this approachunifies two former approaches to Br\`{e}gman relative entropy: one based onreflexive Banach spaces, another based on differential geometry. Thisconstruction allows to extend Br\`{e}gman relative entropies, and relatedgeometric and operator structures, to arbitrary-dimensional state spaces ofprobability, quantum, and postquantum theory. We give several examples, notconsidered previously in the literature.

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