TY - JOUR
T1 - Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos
AU - Borges, Ernesto P.
AU - Tsallis, Constantino
AU - Añaños, Garín F.J.
AU - de Oliveira, Paulo Murilo C.
N1 - 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).
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037122313&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.89.254103
DO - 10.1103/PhysRevLett.89.254103
M3 - Artículo
AN - SCOPUS:0037122313
SN - 0031-9007
VL - 89
JO - Physical Review Letters
JF - Physical Review Letters
IS - 25
ER -