MPIDS Seminar: Onsager Principle as a Problem Solving Tool

In the celebrated paper on the reciprocal relation for the kinetic coefficients in irreversible thermo-dynamics, Onsager proposed a variational principle that extends Rayleigh's least energy dissipation principle to general irreversible processes. This variational principle has been shown to be very useful in soft matter. Many basic equations in soft matter, such as Smoluchowski equation, Nernst-Fokker-Planck equation, Ericksen-Leslie equation, gel dynamic equation… have all been derived from this principle[1,2]. The principle has also been shown to be useful in getting approximate solutions[3]. In this talk, I will show that the principle can be stated in a more convenient form for application: it can be stated in the form of minimal path principle that “nature chooses the path that minimizes certain time integral of a modified Rayleighian”. I will show that this formulation will open new applications of the Onsager principle to wider classes of problems.
Acknowledgement: This work was motivated by a stimulating discussion with Prof. Hans Crirstian Ottinger (ETH, Zurich).

REFERENCES
1. Masao Doi, Onsager's variational principle in soft matter, J. Phys. Cond Matt. 23 (2011) 284118 1-8
2. Masao Doi, Soft Matter Physics, Oxford University Press, p1-257 (2013)
3. Masao Doi, Onsager principle as a tool for approximation, Chin. Phys. B Vol. 24, 020505, (2015)