title: Entropies for severely contracted configuration space.
abstract: We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index [Formula: see text] describes the contraction process, while the dual index [Formula: see text] defines the contraction dimension at which extensivity is restored. We study this circumstance along the three routes to chaos in low-dimensional nonlinear maps where the attractors at the transitions, between regular and chaotic behavior, drive phase-space contraction for ensembles of trajectories. We illustrate this circumstance for properties of systems that find descriptions in terms of nonlinear maps. These are size-rank functions, urbanization and similar processes, and settings where frequency locking takes place.
authors.affiliation: Department of Physics, Istanbul University, 34134, Vezneciler, Istanbul, Turkey.
authors.forename: G Cigdem
authors.initials: GC
authors.lastname: Yalcin
authors.affiliation: Instituto de Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México 01000 Distrito Federal, Mexico.
authors.forename: Carlos
authors.initials: C
authors.lastname: Velarde
authors.affiliation: Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México 01000 Distrito Federal, Mexico.
authors.forename: Alberto
authors.initials: A
authors.lastname: Robledo
keywords: Nonlinear dynamical systems; Nonlinear physics; Physics; Statistical physics