Remarks about the microcanonical description of astrophysical systems

We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling laws of the thermodynamical variables and potentials in the thermodynamic limit. Geometrical considerations motivate a way by means of which could be carried out a well-defined generalized canonical-like description for this kind of systems, even being nonextensive. This interesting possibility allows us to extend the applicability of the Standard Thermodynamic methods, even in the cases in which the system exhibits a negative specific heat. As example of application, we reconsider the classical Antonov problem of the isothermal spheres.