An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q - 1 (entropic nonextensivity) as a simple and efficient manner to provide, at least for some classes of systems, some...

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 $ARCH$)...

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.

A fundamental prebiotic stage of the origin of life is the formation, from a random assembly of oligomers, of information-containing self-replicating polymers. By adopting a growth mechanism (already used by Anderson and others) essentially based in the complementarity of the Crick and Watson...

Within a recently generalized statistical mechanics, we have calculated the specific heat of a classical and quantum anisotropic rigid rotator.

We briefly review, with regard to physical applications, the present status of the recently introduced non-extensive thermostatistics characterized by the entropic index q (q = 1 corresponds to standard, extensive, Boltzmann-Gibbs thermostatistics). In addition to that, we comment on (i) how...