After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index qmix⩽1) and equilibration (characterized by the entropic index qeq⩾1) play central and inter-related roles, and appear to...

We present a Monte Carlo study of a linear chain (d=1) with long-range bonds whose occupancy probabilities are given by pij=p/rijα(0⩽p⩽1;α⩾0) where rij=1,2,… is the distance between sites. The α→∞(α=0) corresponds to the first-neighbor (“mean field”) particular case. We...

We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys. Rev. Lett. 64 (1990)...

In order to discuss some prebiotic stages, we present computer simulations assuming an autocatalytic polymerization of RNA-like chains from a random collection of oligomers in two dimensions through an equilibrium process. In the simulations we consider the effect of the possible cross-links...

The Gibbs–Jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form Sand of physically appropriate constraints. For instance, for the usual canonical ensemble, one adopts (i) S1=−k∑ipilnpi, (ii) ∑ipi=1, and (iii) ∑ipiεi=U1 ({εi}≡...

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state σi(t)∈{0,1} of a cell i does not only depend on the states in its local neighborhood at time t-1, but also on the memory of its own past states σi(t-2),σi(t-3),…,σi(t-τ),… . We assume...

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\in \Re)$ ($S_{1} \equiv...

Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter $b$ ($b=0$ corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a...

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular...

The $GARCH$ algorithm is the most renowned generalisation of Engle's original proposal for modelising {\it returns}, the $ARCH$ process. Both cases are characterised by presenting a time dependent and correlated variance or {\it volatility}. Besides a memory parameter, $b$, (present in $ARCH$)...