  In this paper, we proved that by choosing the proper variational function and
variables, the variational approach proposed by M. Doi in soft matter physics
was equivalent to the Conservation-Dissipation Formalism. To illustrate the
correspondence between these two theories, several novel examples in soft
matter physics, including particle diffusion in dilute solutions, polymer phase
separation dynamics and nematic liquid crystal flows, were carefully examined.
Based on our work, a deep connection among the generalized Gibbs relation, the
second law of thermodynamics and the variational principle in non-equilibrium
thermodynamics was revealed.
