Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems

Masao Doi, Jiajia Zhou, Yana Di, and Xianmin Xu
Phys. Rev. E 99, 063303 – Published 10 June 2019

Abstract

In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for nonequilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic equations, but our previous method has a weakness that it can be justified, strictly speaking, only for small incremental time. Here we propose an improved method which does not have this drawback. The improved method utilizes the integral proposed by Onsager and Machlup in 1953, and can tell us which of the approximate solutions is the best solution without knowing the exact solution. The improved method has an advantage that it allows us to determine the steady state in nonequilibrium system by a variational calculus. We demonstrate this using three examples, (a) simple diffusion problem, (b) capillary problem in a tube with corners, and (c) free boundary problem in liquid coating, for which the kinetic equations are written in second or fourth-order partial differential equations.

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  • Received 26 February 2019
  • Corrected 11 June 2020

DOI:https://doi.org/10.1103/PhysRevE.99.063303

©2019 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft Matter

Corrections

11 June 2020

Correction: A footnote indicating the email address for the corresponding author was missing and has been inserted.

Authors & Affiliations

Masao Doi and Jiajia Zhou*

  • Center of Soft Matter Physics and its Applications, Beihang University, 37 Xueyuan Road, Beijing 100191, China

Yana Di and Xianmin Xu

  • LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

  • *jjzhou@buaa.edu.cn

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Issue

Vol. 99, Iss. 6 — June 2019

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