  An unified thermodynamical framework based in the use of a generalized
Massieu-Planck thermodynamic potential is proposed and a new formulation of
Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a
generalization of (classical) Boltzmann-Gibbs thermostatistics is suggested and
connected to recent nonextensive statistics formulations. This is accomplished
by defining a convenient squeezing function which restricts among the
collections of Boltzmann-Gibbs configurations of the complete equilibrium
closure. The formalism embodies Beck-Cohen superstatistics and a direct
connection with the nonlinear kinetic theory due to Kaniadakis is provided,
being the treatment presented fully consistent with it. As an example Tsallis
nonextensive statistics is completely rebuilt into our formulation adding new
insights (zeroth law of thermodynamics, non ad hoc definition of the mean value
of a physical quantity,...). We relate all the formal development to physical
and measurable quantities and suggest a way to establish the relevant
statistics of any system based on determinations of temperature.
