title: Generalized extensive entropies for studying dynamical systems in highly anisotropic phase spaces.
abstract: Starting from the geometrical interpretation of the Rényi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle with generalized entropies. We prove that for a large class of dynamical systems subject to random perturbations, including particle transport in random media, these entropies play the role of Liapunov functionals. Some physical examples, which can be treated by the generalized Rényi entropies, are also illustrated.
authors.affiliation: Université Libre de Bruxelles (ULB), Department of Physics, Bvd du Triomphe, Campus de la Plaine CP 231, 1050 Brussels, Belgium and Royal Military School (RMS), Av. de la Renaissance 30, 1000 Brussels, Belgium.
authors.forename: Giorgio
authors.initials: G
authors.lastname: Sonnino
authors.affiliation: Association EURATOM-MEdC, University of Craiova, A. I. Cuza 13, 200585 Craiova, Romania.
authors.forename: György
authors.initials: G
authors.lastname: Steinbrecher
mesh_terms: D016880:Anisotropy; D019277:Entropy; D015233:Models, Statistical