Examples of the application of nonparametric information geometry to statistical physics

DOI10.3390/e15104042zbMath1346.35144arXiv1308.5312OpenAlexW3102391787MaRDI QIDQ280599

Giovanni Pistone

Publication date: 10 May 2016

Published in: Entropy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.5312

zbMATH Keywords

Boltzmann equationOrlicz spacesKullback-Leibler divergenceinformation geometryBoltzmann-Gibbs entropydifferential (statistical) connectionsexponential manifoldnon-parametric statistical manifolds

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Global differential geometry (53C99) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Measures of information, entropy (94A17) Boltzmann equations (35Q20)

Related Items (12)

New results on mixture and exponential models by Orlicz spaces ⋮ Information geometry formalism for the spatially homogeneous Boltzmann equation ⋮ Exponential models by Orlicz spaces and applications ⋮ Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space ⋮ Lagrangian and Hamiltonian dynamics for probabilities on the statistical bundle ⋮ Unnamed Item ⋮ Information Geometry of the Probability Simplex: A Short Course ⋮ Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities ⋮ The Banach manifold of measures and the Lagrange multipliers of statistical mechanics ⋮ An eikonal equation approach to thermodynamics and the gradient flows in information geometry ⋮ Unnamed Item ⋮ A Lecture About the Use of Orlicz Spaces in Information Geometry

Cites Work

• Deformed exponentials and applications to finance
• On \(\varphi \)-families of probability distributions
• Orlicz spaces and modular spaces
• Exponential statistical manifold
• Dual connections in nonparametric classical information geometry
• \(\kappa \)-exponential models from the geometrical viewpoint
• Further comments on some comments on a paper by Bradley Efron
• The exponential statistical manifold: mean parameters, orthogonality and space transformations
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• On applications of Orlicz spaces to statistical physics
• Information geometry and sufficient statistics
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE L^p-SPACES
• Unnamed Item
• Unnamed Item

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