eng Science and Education Publishing Applied Mathematics and Physics 2333-4886 2021-08-10 9 1 10 15 10.12691/amp-9-1-3 AMP2021913 article Michael Grinfeld michael.grinfeld4.civ@mail.mil 1 Pavel Grinfeld 2 The U.S. Army Research Laboratory, Aberdeen Proving Ground, USA Mathematics Department, Drexel University, Philadelphia, USA Based on appropriately generalized Gibbs¡¯ variational methodology, we analyzed two-component systems with electrostatic interaction. We begin by formulating isoperimetric-type variational problems, and then proceed with calculation of the first and second variations of the corresponding functionals. The first variation is used for establishing the conditions of equilibrium of the systems under study, whereas the second ¨C is for establishing conditions of stability of equilibrium configurations. The established conditions of equilibrium permit calculating distributions of the mass densities of the components as well as distributions of entropy (or temperature) and the electric potential. To that end, we have to solve a system of four integral equations and one algebraic. http://pubs.sciepub.com/amp/9/1/3/amp-9-1-3.pdf plasma thermodynamics Gibbs variational principles plasma stability equations of state