Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

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dc.creatorBorges, Ernesto P.
dc.creatorTsallis, Constantino
dc.creatorAnanos, Garin F. J.
dc.creatorde Oliveira, Paulo Murilo C.
dc.date2002-03-16
dc.date2002-12-28
dc.date.accessioned2026-07-07T02:44:43Z
dc.date.available2026-07-07T02:44:43Z
dc.descriptionWe consider nonequilibrium probabilistic dynamics in logistic-like 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 $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. 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.
dc.descriptionFinal version with new Title and small modifications. REVTeX, 8 pages and 4 eps figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0203342
dc.identifierhttp://arxiv.org/abs/cond-mat/0203342
dc.identifierPhys. Rev. Lett. 89, 254103 (2002)
dc.identifierdoi:10.1103/PhysRevLett.89.254103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/19040
dc.subjectStatistical Mechanics
dc.titleNonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos
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