Modeling of stability of electrostatic and magnetostatic systems: Analysis based on Gibbs methodology

Models, based on variational principles, provide for multiple features which of key importance for computational implementation. Based on this vision, we combine the Gibbsian thermodynamic (variational) method for heterogeneous systems with electrostatics. The substances under study are those which are able to accumulate free (i.e., not dipolar) electric charges. We announce several key formulas related to the first and second energy variations for these macroscopic heterogeneous systems.