The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1. General Conditions of Equilibrium and Stability for One-Component Charged Gas

Report No. ARL-TR-8348
Authors: Michael Grinfeld; Pavel Grinfeld
Date/Pages: April 2018; 24 pages
Abstract: In this report, we study the equilibrium and stability conditions of one-component charged gas using the Gibbs variational principles. We established the general equations allowing us to analyze the equilibrium conditions of the systems, which contain electrically charged constituents. For the sake of simplicity, technical transparency, and brevity, we limited ourselves to the systems containing the charges of a one sign. Our approach was based on the variational principles of Gibbs, which, in turn, are based on the concept of heterogeneous systems. The deduction of equations of equilibrium is based on the calculation of the first energy variation of the functionals with isoperimetric constraints. We established necessary conditions of thermodynamic stability of the corresponding equilibrium configurations and demonstrated how the concept of stability can be applied to the classical problem of thermodynamic inequalities. We also established the novel thermodynamic inequalities, which generalize the classical thermodynamic inequalities of Gibbs for the charges liquids or gases.
Distribution: Approved for public release
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Last Update / Reviewed: April 1, 2018