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In the present paper we compare the theory of mixtures based on RationalThermomechanics with the one obtained by Hamilton principle. We prove that thetwo theories coincide in the adiabatic case when the action is constructed withthe intrinsic Lagrangian. In the complete thermodynamical case we show that wehave also coincidence in the case of low temperature when the second soundphenomena arises for superfluid Helium and crystals.

Hamiltonian Principle in Binary Mixtures of Euler Fluids with Applications to the Second Sound Phenomena