  We present a new phase-field formulation for the non-equilibrium interface
kinetics. The diffuse interface is considered an integral of numerous
representative volume elements (RVEs), in which there is a two-phase mixture
with two conserved and two non-conserved concentration fields. This particular
way of separating concentration fields leads to two distinct dissipative
processes besides the phase boundary migration, i.e., trans-sharp-interface
diffusion between different phases within a single RVE and
trans-diffuse-interface diffusion between different RVEs within a single phase.
A two-part mechanism is proposed to balance the driving forces and energy
dissipation for diffusionless and diffusional processes in RVEs. Moreover, the
classical interface friction and solute drag can be recovered by integrating
the diffuse interface. Compared with the sharp interface theory, the present
diffuse interface can reproduce the atomic simulated partial-drag
self-consistently in thermodynamics.
