Generalization of the maximum entropy principle for curved statistical manifolds

The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, standard form MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited for many scenarios interest. As a principled approach extend reach MEP, this paper revisits foundations in information geometry shows how curved statistical manifolds naturally leads generalization based on R\'enyi entropy. By establishing bridge between non-Euclidean our proposal sets solid foundation numerous applications entropy, enables range novel systems analysis.