On the statistical theory of strong electrolytes and high-temperature plasmas: new applications of the work of Yukhnovskii and Kelbg

Remembering here the work of two pioneers of the statistical physics of Coulomb systems, G\"unter Kelbg, and Ihor Yukhnovskii, we analyze their methods and give some new applications to ionic solutions and quantum plasmas. In particular, we develop applications of the theory to strong electrolytes and to thermal high-temperature plasmas at $T > 0^5$ K using the exponential interaction model. We show the strong structural similarity of these two classes of Coulomb systems, which physics is determined mostly by contributions proportional to $e^4$ and $e^6$. We predict at higher densities a structural transition to oscillating correlations. The thermodynamic functions show a smooth transition from a quadratic root increase to a slower increase like $n_i^{1/4}$ which observes the Onsager bound. Effects of asymmetries in charges and masses are studied with applications to ionic systems with multiple charges and to high-temperature plasmas, in particular, to plasmas with He$^{2+}$-ions.