Nonequilibrium thermodynamics of multicomponent fluids

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We obtained the general evolution equations for the density and mass flux of each component of a multicomponent fluid on the basis of conservation laws and irreversibility, which are required from the thermodynamic laws, as summarized in the Miyazaki-Kitahara-Bedeaux paper and in the book. The idea is that in a multicomponent fluid, internal energy is no more a conservative quantity, but the total energy including the kinetic energy of mass fluxes is conserved. Thus the Gibbs relation is generalized in terms of total energy density. Then the momentum densities ( mass flux densities) enter into the Gibbs relation. Then we derived linear irreversible thermodynamics in terms of intensive parameters, which appear in the generalized Gibbs relation. Furthermore, assuming the reversible part of the evolution equation has a symplectic property, which automatically satisfies the condition of no entropy production, we derived the reversiblepart of the evolution equation, which was not known for the mass flux of multicomponent fluids. Since our formulation is based on the entorpy concept, we generalized Boltzmann-Einstein principle to none quilibrium fluctuation of multicomponent fluids. Especially, thespatial correlation in nonequilibrium reaction-diffusion systems was studied in detail together with computer simulations. Finally, in the frame of linear hydrodynamics, we proved the thermodynamic results are correct from the microscopic Liouville formalism.