12 research outputs found
Nonextensive statistical mechanics, superstatistics and beyond: theory and applications in astrophysical and other complex systems
A brief illustration is presented about the scientific motivation and contributions of this Special Issue
Renormalization group structure for sums of variables generated by incipiently chaotic maps
We look at the limit distributions of sums of deterministic chaotic variables
in unimodal maps and find a remarkable renormalization group (RG) structure
associated to the operation of increment of summands and rescaling. In this
structure - where the only relevant variable is the difference in control
parameter from its value at the transition to chaos - the trivial fixed point
is the Gaussian distribution and a novel nontrivial fixed point is a
multifractal distribution that emulates the Feigenbaum attractor, and is
universal in the sense of the latter. The crossover between the two fixed
points is explained and the flow toward the trivial fixed point is seen to be
comparable to the chaotic band merging sequence. We discuss the nature of the
Central Limit Theorem for deterministic variables.Comment: 14 pages, 5 figures, to appear in Journal of Statistical Mechanic
On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al
In the present paper we refute the criticism advanced in a recent preprint by
Figueiredo et al [1] about the possible application of the -generalized
Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body
classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model.
We exhibit that, contrary to what is claimed by these authors and in accordance
with our previous results, -Gaussian-like curves are possible and real
attractors for a certain class of initial conditions, namely the one which
produces nontrivial longstanding quasi-stationary states before the arrival,
only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for
publication in Europhysics Letters, (2009) in pres
Itineration of the Internet over Nonequilibrium Stationary States in Tsallis Statistics
The cumulative probability distribution of sparseness time interval in the
Internet is studied by the method of data analysis. Round-trip time between a
local host and a destination host through ten odd routers is measured using the
Ping Command, i.e., doing echo experiment. It is found that the data are well
described by the q-exponential destributions, which maximize the Tsallis
entropy indexed by q less or larger than unity. The network is observed to
itinerate over a series of the nonequilibrium stationary states characterized
by Tsallis statistics.Comment: 15 pages, 5 figure
Nonextensivity of the cyclic Lattice Lotka Volterra model
We numerically show that the Lattice Lotka-Volterra model, when realized on a
square lattice support, gives rise to a {\it finite} production, per unit time,
of the nonextensive entropy . This finiteness only occurs for for the growth mode
(growing droplet), and for for the one (growing stripe). This
strong evidence of nonextensivity is consistent with the spontaneous emergence
of local domains of identical particles with fractal boundaries and competing
interactions. Such direct evidence is for the first time exhibited for a
many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure