Conservation-Dissipation Formalism for soft matter physics: I. Augmentation to Doi's variational approach

. In the first paper of this series, we prove that by choosing the proper variational function and variables, the variational approach proposed by Doi in soft matter physics is equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including the particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, are 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 is revealed. Graphical abstract