In a recent paper, we have studied a generalization of the Jensen–Shannon divergence (JSD) (Physica A 329 (2003) 81). This generalization was made in the context of Tsallis’ statistical mechanics. The present work is devoted to an investigation of the metric character of the JSD generalization.

The Jensen–Shannon divergence is a symmetrized and smoothed version of the Kullback–Leibler divergence. Recently it has been widely applied to the analysis and characterization of symbolic sequences. In this paper we investigate a generalization of the Jensen–Shannon divergence. This...

Within a real space renormalization group framework based on self-dual clusters, we discuss the criticality of the quenched bond-mixed q-state Potts ferromagnet on a square lattice. On qualitative grounds we exhibit that crossover from the pure fixed point to the random one occurs, while q...

Using a real space renormalization group method, we calculate the thermal dependence of the susceptibility of the q-state Potts model (ferro- and antiferromagnet) on self-dual Wheatstone-bridge-like hierarchical lattices. The influence of external fields on the antiferromagnetic phase diagram is...

We consider a population with biparental procreation which genetically transmits, through a specific blending-like mechanism, a combination of two characters, namely a nomadic and a sedentary one. Consequently, as time goes on, the population spreads out geographically, space distribution thus...

We study the dynamics of a Hamiltonian system of N classical spins with infinite-range interaction. We present numerical results which confirm the existence of metaequilibrium quasi stationary states (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, Lévy walks...

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 $ARCH$)...

The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory has exibited, along more than one century, great success...

The sensitivity to risk that most people (hence, financial operators) feel affects the dynamics of financial transactions. Here we present an approach to this problem based on a current generalization of Boltzmann-Gibbs statistical mechanics.