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

## TL;DR

This paper demonstrates the equivalence between Doi's variational approach and the Conservation-Dissipation Formalism in soft matter physics, revealing deep thermodynamic connections through examples like particle diffusion and liquid crystal flows.

## Contribution

It establishes a formal equivalence between two theoretical frameworks in soft matter physics and explores their thermodynamic implications.

## Key findings

- Proved the equivalence between Doi's variational approach and Conservation-Dissipation Formalism.
- Illustrated the correspondence with examples in particle diffusion, polymer dynamics, and liquid crystals.
- Revealed the connection among Gibbs relation, second law, and variational principles in non-equilibrium thermodynamics.

## Abstract

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.