The nonadditive entropy S q has been introduced in 1988 focusing on a generalization of
Boltzmann–Gibbs (BG) statistical mechanics. The aim was to cover a (possibly wide) class of …

Metaphors, generalizations and unifications are natural and desirable ingredients of the
evolution of scientific theories and concepts. Physics, in particular, obviously walks along …

As early as 1902, Gibbs pointed out that systems whose partition function diverges, eg
gravitation, lie outside the validity of the Boltzmann–Gibbs (BG) theory. Consistently, since …

Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the
research of the foundations of statistical mechanics. This generalization of the well-known …

The only integrative approach to chaos and random fractal theory Chaos and random fractal
theory are two of the most important theories developed for data analysis. Until now, there …

The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical
mechanics is focused on along a historical perspective. It is then formally enlarged in order …

The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to
construct the exact differential dS= δ Q/T, where δ Q is the heat transfer and the absolute …

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were
generalized, three decades ago, on the basis of the nonadditive entropy S q (q∈ R), which …

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages,
naturally leads to Boltzmann–Gibbs (BG) statistical mechanics, hence to standard …

The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics
can be seen through three different stages. First, the proposal of an entropic functional (S …