  Astrophysical systems will never be in a real Thermodynamic equilibrium: they
undergo an evaporation process due to the fact that the gravity is not able to
confine the particles. Ordinarily, this difficulty is overcome by enclosing the
system in a rigid container which avoids the evaporation. We proposed an
energetic prescription which is able to confine the particles, leading in this
way to an alternative version of the Antonov isothermal model which unifies the
well-known isothermal and polytropic profiles. Besides of the main features of
the isothermal sphere model: the existence of the gravitational collapse and
the energetic region with a negative specific heat, this alternative model has
the advantage that the system size naturally appears as a consequence of the
particles evaporation.
