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

Ernesto P. Borges, Constantino Tsallis, Garín F.J. Añaños, Paulo Murilo C. de Oliveira

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Abstract

We consider nonequilibrium probabilistic dynamics in logisticlike maps [Formula presented], [Formula presented] at their chaos threshold: We first introduce many initial conditions within one among [Formula presented] intervals partitioning the phase space and focus on the unique value [Formula presented] for which the entropic form [Formula presented] linearly increases with time. We then verify that [Formula presented] vanishes like [Formula presented] [[Formula presented]]. We finally exhibit a new finite-size scaling, [Formula presented]. 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.

Original languageEnglish
JournalPhysical Review Letters
Volume89
Issue number25
DOIs
StatePublished - 2002

Bibliographical note

Funding Information:
One of us (C. T.) thanks H. J. Herrmann for fruitful remarks. This work is partially supported by PRONEX/MCT, CNPq, CAPES, and FAPERJ (Brazilian agencies).

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

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