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

Conservation-Dissipation Formalism for Soft Matter Physics: I. Equivalence with Doi's Variational Approach