On compatibility of the natural configuration framework with general equation for non-equilibrium reversible–irreversible coupling (GENERIC): Derivation of anisotropic rate-type models

Abstract

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible). • Equilibrium thermodynamics is considered to be a closed theory • Non-equilibrium thermodynamics, on the contrary, is not • In many frameworks an intensive research has been conducted separately • However, less attention is paid to their relation and general understanding • We compare the Natural Configuration framework and GENERIC on particular models