  Applying Gibb's geometrical methods to the thermodynamics of H-plasmas we
explore the landscape of the free energy as a function of the degrees of
ionization and dissociation. Several approximations for the free energy are
discussed. We show that in the region of partial ionization/dissociation the
quantum Debye-Hueckel approximation (QDHA) yields a rather good but still
simple representation which allows to include magnetic field and fluctuation
effects. By using relations of Onsager-Landau-type the probability of
fluctuations and ionization/dissociation processes are described. We show that
the degrees of ionization/dissociation are probabilistic quantities which are
subject to a relatively large dispersion. Magnetic field effects are studied.
