The criteria for intrinsic thermodynamic stability are obtained for an elastically stressed coherent system comprised of homogeneous phases at equilibrium using the thermodynamic approach of Tisza. The coherency constraint is an additional constraint on admissible thermodynamic perturbations. Thermodynamic densities cannot be perturbed independently and the extremized free energy at equilibrium is no longer convex in all cases. Multiple equilibrium states become possible for certain mechanical boundary conditions. The stability criteria are applied to a binary system possessing a consolute critical point and, in contrast to coherent equilibria among phases with different crystal structures, multiple equilibrium states are shown not to exist in a coherent binary syste, possessing a consolute critical point.
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