Quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and Jacobi fields
From MaRDI portal
Publication:633725
DOI10.1016/j.physd.2010.11.013zbMath1217.37079arXiv1011.5555OpenAlexW2077048218MaRDI QIDQ633725
Publication date: 29 March 2011
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1011.5555
Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Topological entropy (37B40)
Related Items (11)
Softening the Complexity of Entropic Motion on Curved Statistical Manifolds ⋮ Application of the maximum relative entropy method to the physics of ferromagnetic materials ⋮ Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations ⋮ An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information ⋮ Information geometric complexity of a trivariate Gaussian statistical model ⋮ Notions of the ergodic hierarchy for curved statistical manifolds ⋮ Hermite-Gaussian model for quantum states ⋮ Qubit geodesics on the Bloch sphere from optimal-speed Hamiltonian evolutions ⋮ Theoretical investigations of an information geometric approach to complexity ⋮ Learning on dynamic statistical manifolds ⋮ Information geometric complexity of entropic motion on curved statistical manifolds under different metrizations of probability spaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Riemannian geometry of quantum computation
- Information-geometric indicators of chaos in Gaussian Models on statistical manifolds of negative Ricci Curvature
- Stochastic complexity and modeling
- Toward a quantitative theory of self-generated complexity
- Complexities and their applications to characterization of chaos
- Uncertainty, predictability and decidability in chaotic dynamical systems
- What is complexity?
- Measures of statistical complexity: why?
- Jacobi fields on statistical manifolds of negative curvature
- Quantum Computation as Geometry
- The generalized Jacobi equation
- On the complexity of statistical models admitting correlations
- INFORMATION GEOMETRY, INFERENCE METHODS AND CHAOTIC ENERGY LEVELS STATISTICS
- Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
- Chaos and complexity of quantum motion
- How Many “Arrows of Time” Do We Really Need to Comprehend Statistical Laws?
- Logical basis for information theory and probability theory
- On the relation between entropy and the average complexity of trajectories in dynamical systems
This page was built for publication: Quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and Jacobi fields
