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Geometric structures induced by deformations of the legendre transform

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posted on 2024-03-27, 15:32 authored by Pablo A Morales, Jan Korbel, Fernando Ernesto Rosas De AndracaFernando Ernesto Rosas De Andraca
The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi’s divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its implications for physical systems. Here we shed new light on the Legendre transform by revealing the consequences of its deformation via symplectic geometry and complexification. These findings reveal a novel common framework that leads to a principled and unified understanding of physical systems that are not well-described by classic information-theoretic quantities.

History

Publication status

  • Published

File Version

  • Published version

Journal

Entropy

ISSN

1099-4300

Publisher

MDPI AG

Issue

4

Volume

25

Article number

ARTN 678

Department affiliated with

  • Informatics Publications

Institution

University of Sussex

Full text available

  • Yes

Peer reviewed?

  • Yes