Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We analyse the Boltzmann operator in the geometric setting from the point of view 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. In a second part of the paper we discuss a generalization of the Orlicz setting to include spatial derivatives and apply it to the Hyv\"arinen divergence