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Conservation-Dissipation Formalism for soft matter physics: I. Augmentation to Doi's variational approach
Liangrong Peng1,2, Yucheng Hu1, Liu Hong3
1Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, 100084, Beijing, P. R. China.
The European Physical Journal. E, Soft Matter
|June 13, 2019
Summary
This study demonstrates the equivalence between Doi's variational approach and the Conservation-Dissipation Formalism in soft matter physics. This reveals a deep connection within non-equilibrium thermodynamics, linking variational principles to fundamental laws.
Area of Science:
- Soft matter physics
- Non-equilibrium thermodynamics
- Theoretical physics
Background:
- The variational approach by Doi is a key tool in soft matter physics.
- The Conservation-Dissipation Formalism offers an alternative framework for describing dissipative systems.
- Understanding the relationship between these formalisms is crucial for advancing non-equilibrium theories.
Purpose of the Study:
- To establish the theoretical equivalence between Doi's variational approach and the Conservation-Dissipation Formalism.
- To explore novel applications and connections within soft matter physics.
- To elucidate the fundamental links between generalized Gibbs relations, the second law of thermodynamics, and variational principles.
Main Methods:
- Selection of appropriate variational functions and variables.
- Application of the Conservation-Dissipation Formalism.
- Comparative analysis of theoretical frameworks using soft matter examples.
Main Results:
- Proof of the equivalence between Doi's variational approach and the Conservation-Dissipation Formalism.
- Detailed examination of particle diffusion, polymer phase separation, and liquid crystal flows.
- Identification of a profound connection between generalized Gibbs relations, the second law of thermodynamics, and variational principles in non-equilibrium systems.
Conclusions:
- The equivalence provides a unified perspective on non-equilibrium phenomena.
- The findings deepen the understanding of thermodynamic laws within variational frameworks.
- This work offers a robust theoretical foundation for future research in soft matter and non-equilibrium thermodynamics.
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