论文标题
Legendre变换的变形引起的几何结构
Geometric Structures Induced by Deformations of the Legendre Transform
论文作者
论文摘要
广义的Legendre变换与非双性平坦统计流形之间发现的最新链接表明，Rényi的分歧和熵无处不在的基本原因是广泛的物理现象。但是，这些早期发现仍然几乎没有关于这种关系的性质及其对物理系统的影响。在这里，我们通过通过互合式的几何形状和络合率揭示其变形的后果来为Legendre变换提供了新的启示。这些发现揭示了一个新颖的常见框架，该框架导致对物理系统的原则和统一的理解，而经典信息理论数量并未很好地描述。
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.
