title: Nonequilibrium probabilistic dynamics of the logistic map at the edge of chaos.
abstract: We consider nonequilibrium probabilistic dynamics in logisticlike maps x(t+1)=1-a|x(t)|(z), (z>1) at their chaos threshold: We first introduce many initial conditions within one among W>>1 intervals partitioning the phase space and focus on the unique value q(sen)<1 for which the entropic form S(q) identical with (1- summation operator Wp(q)(i))/(q-1) linearly increases with time. We then verify that S(q(sen))(t)-S(q(sen))( infinity ) vanishes like t(-1/[q(rel)(W)-1]) [q(rel)(W)>1]. We finally exhibit a new finite-size scaling, q(rel)( infinity )-q(rel)(W) proportional, variant W(-|q(sen)|). This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
authors.forename: Ernesto P
authors.initials: EP
authors.lastname: Borges
authors.forename: Constantino
authors.initials: C
authors.lastname: Tsallis
authors.forename: Garín F J
authors.initials: GF
authors.lastname: Añaños
authors.forename: Paulo Murilo C
authors.initials: PM
authors.lastname: de Oliveira