On the Gibbs conditions of stable equilibrium, convexity and the second-order variations of thermodynamic potentials in nonlinear thermoelasticity

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The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the convexity or concavity properties of all thermodynamic potentials in relation to each other, and to derive the relationships between the specific heats at constant stress and deformation, and between the isentropic and isothermal elastic moduli and compliances. The comparison with the derivation based on the classical thermodynamic approach is also given.