Remarks on the nonuniversality of Boltzmann-Gibbs statistical mechanics

How general are Boltzmann-Gibbs statistical mechanics and standard Thermodynamics? What classes of systems have thermostatistical properties, in particular equilibrium properties, that are correctly described by these formalisms? The answer is far from trivial. It is, however, clear today that these relevant and popular formalisms are not universal, this is to say that they have a domain of validity that it would be important to define precisely. A few remarks on these questions are herein presented, in particular in relation to nonextensive statistical mechanics, introduced a decade ago with the aim to cover at least some (but most probably not all) of the natural systems that are out of this domain of validity.