  The variational approach usually used in phase field models (PFVA) is applied
here to analyse complex irreversible processes such as thermoelectric (TE)
effects and thermally driven mass transport (TDMT). Complex irreversible
processes arise from the coupling effects between simple irreversible
processes. Each simple irreversible process is assiciated with an entropy or
energy density function. During complex irreversible processes with multiple
fields present, this entropy or energy density function is assumed to be
dependent on all independent field variables. Using the total entropy
functionals, the TE effects and TDMT are analysed and important kinetic
coefficients such as the Seebeck coefficient and the heat of transport are
determined with straightforward physical contents. Using the total energy
functionals, the linear irreversible processes are analysed with the Onsager
approach and the nonlinear irreversible processes with PFVA. It is found both
the Onsager's relations and the fluxes defined using PFVA guarantee the
satisfaction of the first law of thermodynamics during the process of
conversion of energies. To analyze the diffusion process under the influence of
elasticity, PFVA is also modified to incorporate the reversible evolution of
elastic fields. It is shown energies are conserved via both the irreversible
diffusion process and the reversible evolution of the elastic fields. Finally,
PFVA is generalized to study nonequilibrium thermodynamics using an extra
kinetic contribution to the entropy density function. The analyses can be
extended to a nonequilibrium thermodynamic system with multiple physical fields
present. Thus, it is believed PFVA has the potential of not only significantly
advancing our understanding of the thermodynamics of irreversible processes,
but also making thermodynamics as a discipline and the study of it truly
dynamic.
