7 papers
Stäckel and Eisenhart lifts, Haantjes geometry and Gravitation
OndÅej Kubů, Piergiulio Tempesta
We study lifts of integrable systems by means of generalized Stäckel geometry. To this end, we present the notion of Stäckel lift as a unified setting for the construction of new…
Laurent Sequences, Extended Rota Algebras and Categorical Discretization of Dynamical Systems
Miguel A. Rodriguez, Piergiulio Tempesta
We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. T…
Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning
Andrzej Cichocki, Piergiulio Tempesta
We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite…
Universality classes, Thermodynamics of Group Entropies, and Black Holes
Henrik Jeldtoft Jensen, Petr Jizba, Piergiulio Tempesta
Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations grows ex…
Jacobi-Haantjes manifolds, integrability and dissipative mechanical systems
Rafael Azuaje, Piergiulio Tempesta
The notion of Jacobi-Haantjes manifold, consisting of a Jacobi manifold endowed with an algebra of extended Haantjes operator fields, is proposed as a natural geometric framework w…
Group structure as a foundation for entropies
Henrik Jeldtoft Jensen, Piergiulio Tempesta
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be…