It is shown how the free energy can be constructed as functional of the one-body distribution function and the exact statistical-mechanical stability condition is formulated which generalizes the known stability condition for isotropic phases of spherical molecules imposing the positivity of the compressibility. It is shown how this new stability condition which may be interpreted as the title suggests and corresponds to d2F/dS2 > 0 in the mean field Landau-de Gennes theory, is decoupled from the known condition. Examples are given when explicit computation was possible. Extensions of the nematic case to smectics are also explicitly given.