Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
AbstractInformation Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Lods, B.; Pistone, G. Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation. Entropy 2015, 17, 4323-4363.
Lods B, Pistone G. Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation. Entropy. 2015; 17(6):4323-4363.Chicago/Turabian Style
Lods, Bertrand; Pistone, Giovanni. 2015. "Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation." Entropy 17, no. 6: 4323-4363.