Onsager Principle - The Basic and Useful Principle in Soft Matter Physics

Abstract

Onsager principle is a variational principle proposed by Lars ONSAGER in 1931 in his celebrated paper on the reciprocal relation in non-equilibrium thermodynamics _[1]. The principle is very important in soft matter physics _[2,3,4]. Almost all kinetic equations proposed for soft matter systems can be derived from this principle. The principle is also very useful. Being an energy-based principle, it simplifies the process of deriving the set of equations to be solved, like Lagrangian in classical mechanics. Onsager principle also gives us various ways of solving these equations _[5]. Since it is a principle of minimization, it can be used to get approximate solutions of the equations. Here the speaker reviews the principle taking examples from his recent works _[6,7]. 

References 
[1] Onsager L . Reciprocal relations in irreversible processes. I: Phys Rev,37, 405–26 (1931),  II: Phys Rev, 38,2265–79(1931) .
[2] Doi M, and Edwards S. F., The Theory of Polymer Dynamics, Oxford University Press 1-391 (1986)
[3] Doi M., Soft Matter Physics, Oxford University Press 1-257 (2013)
[4] Doi M., Onsager principle in polymer dynamics, Progress in Polymer Science 112, 101339 (2020)
[5] Doi M., Onsager principle as a tool for approximation, Chinese Physics B, 24,020505 1-6  (2015)
[6] Zhou J. and Doi M., Dynamics of Viscoelastic Filaments Based on Onsager Principle, Physical Review F, 3, 084004 1-21 (2018) 
[7] Lyu M. Ding Z. Doi M. and Man X.; A Unified Model for Non-Fickian Diffusion and Anomalous Swelling of Glassy Polymer Gels, ACS Macro Lett. 13, 483−488.(2024)

About the Speaker

Prof. Masao DOI is Emeritus Professor of The University of Tokyo and Nagoya University. He obtained his Doctoral Degree at The University of Tokyo in 1976, before working at Tokyo Metropolitan University, Nagoya University and The University of Tokyo in Japan. From 1976 to 1978, he collaborated with Sam EDWARDS in Cambridge, and proposed the reptation theory which became the base of molecular understanding of the non-linear rheology of flexible polymers in liquid state. He researched on many problems in the dynamics of polymers including rheology of liquid crystalline polymers, diffusion-rheology coupling in gels and polymer solutions, surface rheology (friction and adhesions).  He has written three books, The theory of polymer dynamics (coauthored with Sam Edwards), Introduction and Polymer Physics and Soft Matter Physics, which have been used as a textbooks for polymer and soft matter sciences.

As a pioneer in the field, Prof. Doi has won prestigious awards such as the Polymer Physics Prize (2001, American Physical Society) and the Bingham Medal (2001, The Society of Rheology), and National Member of Engineering (2016, USA). His foundational contributions, most notably the famous Doi-Edwards theory, are standard textbook materials globally.

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