2 research outputs found
Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos
We consider nonequilibrium probabilistic dynamics in logistic-like maps
, at their chaos threshold: We first introduce many
initial conditions within one among intervals partitioning the phase
space and focus on the unique value for which the entropic form
{\it linearly} increases with
time. We then verify that vanishes like
[]. We finally exhibit a new finite-size
scaling, . 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.Comment: Final version with new Title and small modifications. REVTeX, 8 pages
and 4 eps figure
Physical Review Letters
p. 254103-1/4We consider nonequilibrium probabilistic dynamics in logisticlike maps xt+1=1-a|xt|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 qsen<1 for which the entropic form Sq≡(1 ∑i=1Wpiq)/(q-1) linearly increases with time. We then verify that Sqsen(t)-Sqsen(∞) vanishes like t-1/[qrel(W)-1] [qrel(W)>1]. We finally exhibit a new finite-size scaling, qrel(∞)-qrel(W)∝W-|qsen|. 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