This paper systematically presents the λ-deformation as the canonical framework of
deformation to the dually flat (Hessian) geometry, which has been well established in …

Tsallis and Rényi entropies, which are monotone transformations of each other, are
deformations of the celebrated Shannon entropy. Maximization of these deformed entropies …

A deformation is a positive continuous function defined on an appropriate interval. Through
deformations, we generalize the notion of concavity for functions. We introduce the order …

Optimal transport and information geometry both study geometric structures on spaces of
probability distributions. Optimal transport characterizes the cost-minimizing movement from …

This paper reviews the role of convex duality in Information Geometry. It clarifies the notion
of bi-orthogonal coordinates associated with Legendre duality by treating its two underlying …

The maximum entropy principle (MEP) is one of the most prominent methods to investigate
and model complex systems. Despite its popularity, the standard form of the MEP can only …

This paper investigates generalized thermodynamic relationships in physical systems where
relevant macroscopic variables are determined by the exponential Kolmogorov–Nagumo …

The logarithmic divergence is an extension of the Bregman divergence motivated by optimal
transport and a generalized convex duality, and satisfies many remarkable properties. Using …

This chapter investigates deformations to the exponential family and the mixture family of
probability density functions, under both subtractive and divisive normalizations. We study …

A system of ordinary differential equations satisfied by the geometric divergence, a
generalization of the canonical divergence on a dually flat space, is introduced. By using the …