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The variational approach usually used in phase field models (PFVA) is appliedhere to analyse complex irreversible processes such as thermoelectric (TE)effects and thermally driven mass transport (TDMT). Complex irreversibleprocesses arise from the coupling effects between simple irreversibleprocesses. Each simple irreversible process is assiciated with an entropy orenergy density function. During complex irreversible processes with multiplefields present, this entropy or energy density function is assumed to bedependent on all independent field variables. Using the total entropyfunctionals, the TE effects and TDMT are analysed and important kineticcoefficients such as the Seebeck coefficient and the heat of transport aredetermined with straightforward physical contents. Using the total energyfunctionals, the linear irreversible processes are analysed with the Onsagerapproach and the nonlinear irreversible processes with PFVA. It is found boththe Onsager's relations and the fluxes defined using PFVA guarantee thesatisfaction of the first law of thermodynamics during the process ofconversion of energies. To analyze the diffusion process under the influence ofelasticity, PFVA is also modified to incorporate the reversible evolution ofelastic fields. It is shown energies are conserved via both the irreversiblediffusion process and the reversible evolution of the elastic fields. Finally,PFVA is generalized to study nonequilibrium thermodynamics using an extrakinetic contribution to the entropy density function. The analyses can beextended to a nonequilibrium thermodynamic system with multiple physical fieldspresent. Thus, it is believed PFVA has the potential of not only significantlyadvancing our understanding of the thermodynamics of irreversible processes,but also making thermodynamics as a discipline and the study of it trulydynamic.

Analysis on Irreversible Processes using the Phase-Field Variational Approach with the Entropy or Energy Functional