Comparison of methodologies for the application of the Onsager variational principle

Abstract: Doi suggested a way to apply the Onsager variational principle to various complex fluids. However, since the Onsager principle is constructed by a daring generalization of classical irreversible thermodynamics (linear theory of fluxes and forces) in an inductive manner, it is questionable whether it can be applied to complex fluids which need non-classical state variables, which may called internal variables, and may require nonlinear relations between fluxes and forces. Since Doi’s approach is based on isothermal process and the stress formula which is defined from an analogy to an approximate equation for creeping flow, it is restricted to incompressible fluid. Our variational thermodynamics derives the Onsager variational principle in a deductive manner and removes the demerits of the Doi’s application of the Onsager variational principle. Our theory allows that regardless of the user's expertise, simply selecting state variables can automatically determine the arguments of the dissipation function and find the desired constitutive equations.